Identifier
Mp00094: Integer compositions —to binary word⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Images
[1] => 1 => 1
[1,1] => 11 => 11
[2] => 10 => 01
[1,1,1] => 111 => 111
[1,2] => 110 => 101
[2,1] => 101 => 011
[3] => 100 => 001
[1,1,1,1] => 1111 => 1111
[1,1,2] => 1110 => 1101
[1,2,1] => 1101 => 1011
[1,3] => 1100 => 1001
[2,1,1] => 1011 => 0111
[2,2] => 1010 => 0101
[3,1] => 1001 => 0011
[4] => 1000 => 0001
[1,1,1,1,1] => 11111 => 11111
[1,1,1,2] => 11110 => 11101
[1,1,2,1] => 11101 => 11011
[1,1,3] => 11100 => 11001
[1,2,1,1] => 11011 => 10111
[1,2,2] => 11010 => 10101
[1,3,1] => 11001 => 10011
[1,4] => 11000 => 10001
[2,1,1,1] => 10111 => 01111
[2,1,2] => 10110 => 01101
[2,2,1] => 10101 => 01011
[2,3] => 10100 => 01001
[3,1,1] => 10011 => 00111
[3,2] => 10010 => 00101
[4,1] => 10001 => 00011
[5] => 10000 => 00001
[1,1,1,1,1,1] => 111111 => 111111
[1,1,1,1,2] => 111110 => 111101
[1,1,1,2,1] => 111101 => 111011
[1,1,1,3] => 111100 => 111001
[1,1,2,1,1] => 111011 => 110111
[1,1,2,2] => 111010 => 110101
[1,1,3,1] => 111001 => 110011
[1,1,4] => 111000 => 110001
[1,2,1,1,1] => 110111 => 101111
[1,2,1,2] => 110110 => 101101
[1,2,2,1] => 110101 => 101011
[1,2,3] => 110100 => 101001
[1,3,1,1] => 110011 => 100111
[1,3,2] => 110010 => 100101
[1,4,1] => 110001 => 100011
[1,5] => 110000 => 100001
[2,1,1,1,1] => 101111 => 011111
[2,1,1,2] => 101110 => 011101
[2,1,2,1] => 101101 => 011011
[2,1,3] => 101100 => 011001
[2,2,1,1] => 101011 => 010111
[2,2,2] => 101010 => 010101
[2,3,1] => 101001 => 010011
[2,4] => 101000 => 010001
[3,1,1,1] => 100111 => 001111
[3,1,2] => 100110 => 001101
[3,2,1] => 100101 => 001011
[3,3] => 100100 => 001001
[4,1,1] => 100011 => 000111
[4,2] => 100010 => 000101
[5,1] => 100001 => 000011
[6] => 100000 => 000001
[1,1,1,1,1,1,1] => 1111111 => 1111111
[1,1,1,1,1,2] => 1111110 => 1111101
[1,1,1,1,2,1] => 1111101 => 1111011
[1,1,1,1,3] => 1111100 => 1111001
[1,1,1,2,1,1] => 1111011 => 1110111
[1,1,1,2,2] => 1111010 => 1110101
[1,1,1,3,1] => 1111001 => 1110011
[1,1,1,4] => 1111000 => 1110001
[1,1,2,1,1,1] => 1110111 => 1101111
[1,1,2,1,2] => 1110110 => 1101101
[1,1,2,2,1] => 1110101 => 1101011
[1,1,2,3] => 1110100 => 1101001
[1,1,3,1,1] => 1110011 => 1100111
[1,1,3,2] => 1110010 => 1100101
[1,1,4,1] => 1110001 => 1100011
[1,1,5] => 1110000 => 1100001
[1,2,1,1,1,1] => 1101111 => 1011111
[1,2,1,1,2] => 1101110 => 1011101
[1,2,1,2,1] => 1101101 => 1011011
[1,2,1,3] => 1101100 => 1011001
[1,2,2,1,1] => 1101011 => 1010111
[1,2,2,2] => 1101010 => 1010101
[1,2,3,1] => 1101001 => 1010011
[1,2,4] => 1101000 => 1010001
[1,3,1,1,1] => 1100111 => 1001111
[1,3,1,2] => 1100110 => 1001101
[1,3,2,1] => 1100101 => 1001011
[1,3,3] => 1100100 => 1001001
[1,4,1,1] => 1100011 => 1000111
[1,4,2] => 1100010 => 1000101
[1,5,1] => 1100001 => 1000011
[1,6] => 1100000 => 1000001
[2,1,1,1,1,1] => 1011111 => 0111111
[2,1,1,1,2] => 1011110 => 0111101
[2,1,1,2,1] => 1011101 => 0111011
[2,1,1,3] => 1011100 => 0111001
[2,1,2,1,1] => 1011011 => 0110111
[2,1,2,2] => 1011010 => 0110101
>>> Load all 1216 entries. <<<
[2,1,3,1] => 1011001 => 0110011
[2,1,4] => 1011000 => 0110001
[2,2,1,1,1] => 1010111 => 0101111
[2,2,1,2] => 1010110 => 0101101
[2,2,2,1] => 1010101 => 0101011
[2,2,3] => 1010100 => 0101001
[2,3,1,1] => 1010011 => 0100111
[2,3,2] => 1010010 => 0100101
[2,4,1] => 1010001 => 0100011
[2,5] => 1010000 => 0100001
[3,1,1,1,1] => 1001111 => 0011111
[3,1,1,2] => 1001110 => 0011101
[3,1,2,1] => 1001101 => 0011011
[3,1,3] => 1001100 => 0011001
[3,2,1,1] => 1001011 => 0010111
[3,2,2] => 1001010 => 0010101
[3,3,1] => 1001001 => 0010011
[3,4] => 1001000 => 0010001
[4,1,1,1] => 1000111 => 0001111
[4,1,2] => 1000110 => 0001101
[4,2,1] => 1000101 => 0001011
[4,3] => 1000100 => 0001001
[5,1,1] => 1000011 => 0000111
[5,2] => 1000010 => 0000101
[6,1] => 1000001 => 0000011
[7] => 1000000 => 0000001
[1,1,1,1,1,1,1,1] => 11111111 => 11111111
[1,1,1,1,1,1,2] => 11111110 => 11111101
[1,1,1,1,1,2,1] => 11111101 => 11111011
[1,1,1,1,1,3] => 11111100 => 11111001
[1,1,1,1,2,1,1] => 11111011 => 11110111
[1,1,1,1,2,2] => 11111010 => 11110101
[1,1,1,1,3,1] => 11111001 => 11110011
[1,1,1,1,4] => 11111000 => 11110001
[1,1,1,2,1,1,1] => 11110111 => 11101111
[1,1,1,2,1,2] => 11110110 => 11101101
[1,1,1,2,2,1] => 11110101 => 11101011
[1,1,1,2,3] => 11110100 => 11101001
[1,1,1,3,1,1] => 11110011 => 11100111
[1,1,1,3,2] => 11110010 => 11100101
[1,1,1,4,1] => 11110001 => 11100011
[1,1,1,5] => 11110000 => 11100001
[1,1,2,1,1,1,1] => 11101111 => 11011111
[1,1,2,1,1,2] => 11101110 => 11011101
[1,1,2,1,2,1] => 11101101 => 11011011
[1,1,2,1,3] => 11101100 => 11011001
[1,1,2,2,1,1] => 11101011 => 11010111
[1,1,2,2,2] => 11101010 => 11010101
[1,1,2,3,1] => 11101001 => 11010011
[1,1,2,4] => 11101000 => 11010001
[1,1,3,1,1,1] => 11100111 => 11001111
[1,1,3,1,2] => 11100110 => 11001101
[1,1,3,2,1] => 11100101 => 11001011
[1,1,3,3] => 11100100 => 11001001
[1,1,4,1,1] => 11100011 => 11000111
[1,1,4,2] => 11100010 => 11000101
[1,1,5,1] => 11100001 => 11000011
[1,1,6] => 11100000 => 11000001
[1,2,1,1,1,1,1] => 11011111 => 10111111
[1,2,1,1,1,2] => 11011110 => 10111101
[1,2,1,1,2,1] => 11011101 => 10111011
[1,2,1,1,3] => 11011100 => 10111001
[1,2,1,2,1,1] => 11011011 => 10110111
[1,2,1,2,2] => 11011010 => 10110101
[1,2,1,3,1] => 11011001 => 10110011
[1,2,1,4] => 11011000 => 10110001
[1,2,2,1,1,1] => 11010111 => 10101111
[1,2,2,1,2] => 11010110 => 10101101
[1,2,2,2,1] => 11010101 => 10101011
[1,2,2,3] => 11010100 => 10101001
[1,2,3,1,1] => 11010011 => 10100111
[1,2,3,2] => 11010010 => 10100101
[1,2,4,1] => 11010001 => 10100011
[1,2,5] => 11010000 => 10100001
[1,3,1,1,1,1] => 11001111 => 10011111
[1,3,1,1,2] => 11001110 => 10011101
[1,3,1,2,1] => 11001101 => 10011011
[1,3,1,3] => 11001100 => 10011001
[1,3,2,1,1] => 11001011 => 10010111
[1,3,2,2] => 11001010 => 10010101
[1,3,3,1] => 11001001 => 10010011
[1,3,4] => 11001000 => 10010001
[1,4,1,1,1] => 11000111 => 10001111
[1,4,1,2] => 11000110 => 10001101
[1,4,2,1] => 11000101 => 10001011
[1,4,3] => 11000100 => 10001001
[1,5,1,1] => 11000011 => 10000111
[1,5,2] => 11000010 => 10000101
[1,6,1] => 11000001 => 10000011
[1,7] => 11000000 => 10000001
[2,1,1,1,1,1,1] => 10111111 => 01111111
[2,1,1,1,1,2] => 10111110 => 01111101
[2,1,1,1,2,1] => 10111101 => 01111011
[2,1,1,1,3] => 10111100 => 01111001
[2,1,1,2,1,1] => 10111011 => 01110111
[2,1,1,2,2] => 10111010 => 01110101
[2,1,1,3,1] => 10111001 => 01110011
[2,1,1,4] => 10111000 => 01110001
[2,1,2,1,1,1] => 10110111 => 01101111
[2,1,2,1,2] => 10110110 => 01101101
[2,1,2,2,1] => 10110101 => 01101011
[2,1,2,3] => 10110100 => 01101001
[2,1,3,1,1] => 10110011 => 01100111
[2,1,3,2] => 10110010 => 01100101
[2,1,4,1] => 10110001 => 01100011
[2,1,5] => 10110000 => 01100001
[2,2,1,1,1,1] => 10101111 => 01011111
[2,2,1,1,2] => 10101110 => 01011101
[2,2,1,2,1] => 10101101 => 01011011
[2,2,1,3] => 10101100 => 01011001
[2,2,2,1,1] => 10101011 => 01010111
[2,2,2,2] => 10101010 => 01010101
[2,2,3,1] => 10101001 => 01010011
[2,2,4] => 10101000 => 01010001
[2,3,1,1,1] => 10100111 => 01001111
[2,3,1,2] => 10100110 => 01001101
[2,3,2,1] => 10100101 => 01001011
[2,3,3] => 10100100 => 01001001
[2,4,1,1] => 10100011 => 01000111
[2,4,2] => 10100010 => 01000101
[2,5,1] => 10100001 => 01000011
[2,6] => 10100000 => 01000001
[3,1,1,1,1,1] => 10011111 => 00111111
[3,1,1,1,2] => 10011110 => 00111101
[3,1,1,2,1] => 10011101 => 00111011
[3,1,1,3] => 10011100 => 00111001
[3,1,2,1,1] => 10011011 => 00110111
[3,1,2,2] => 10011010 => 00110101
[3,1,3,1] => 10011001 => 00110011
[3,1,4] => 10011000 => 00110001
[3,2,1,1,1] => 10010111 => 00101111
[3,2,1,2] => 10010110 => 00101101
[3,2,2,1] => 10010101 => 00101011
[3,2,3] => 10010100 => 00101001
[3,3,1,1] => 10010011 => 00100111
[3,3,2] => 10010010 => 00100101
[3,4,1] => 10010001 => 00100011
[3,5] => 10010000 => 00100001
[4,1,1,1,1] => 10001111 => 00011111
[4,1,1,2] => 10001110 => 00011101
[4,1,2,1] => 10001101 => 00011011
[4,1,3] => 10001100 => 00011001
[4,2,1,1] => 10001011 => 00010111
[4,2,2] => 10001010 => 00010101
[4,3,1] => 10001001 => 00010011
[4,4] => 10001000 => 00010001
[5,1,1,1] => 10000111 => 00001111
[5,1,2] => 10000110 => 00001101
[5,2,1] => 10000101 => 00001011
[5,3] => 10000100 => 00001001
[6,1,1] => 10000011 => 00000111
[6,2] => 10000010 => 00000101
[7,1] => 10000001 => 00000011
[8] => 10000000 => 00000001
[1,1,1,1,1,1,1,1,1] => 111111111 => 111111111
[1,1,1,1,1,1,1,2] => 111111110 => 111111101
[1,1,1,1,1,1,2,1] => 111111101 => 111111011
[1,1,1,1,1,1,3] => 111111100 => 111111001
[1,1,1,1,1,2,1,1] => 111111011 => 111110111
[1,1,1,1,1,2,2] => 111111010 => 111110101
[1,1,1,1,1,3,1] => 111111001 => 111110011
[1,1,1,1,1,4] => 111111000 => 111110001
[1,1,1,1,2,1,1,1] => 111110111 => 111101111
[1,1,1,1,2,1,2] => 111110110 => 111101101
[1,1,1,1,2,2,1] => 111110101 => 111101011
[1,1,1,1,2,3] => 111110100 => 111101001
[1,1,1,1,3,1,1] => 111110011 => 111100111
[1,1,1,1,3,2] => 111110010 => 111100101
[1,1,1,1,4,1] => 111110001 => 111100011
[1,1,1,1,5] => 111110000 => 111100001
[1,1,1,2,1,1,1,1] => 111101111 => 111011111
[1,1,1,2,1,1,2] => 111101110 => 111011101
[1,1,1,2,1,2,1] => 111101101 => 111011011
[1,1,1,2,1,3] => 111101100 => 111011001
[1,1,1,2,2,1,1] => 111101011 => 111010111
[1,1,1,2,2,2] => 111101010 => 111010101
[1,1,1,2,3,1] => 111101001 => 111010011
[1,1,1,2,4] => 111101000 => 111010001
[1,1,1,3,1,1,1] => 111100111 => 111001111
[1,1,1,3,1,2] => 111100110 => 111001101
[1,1,1,3,2,1] => 111100101 => 111001011
[1,1,1,3,3] => 111100100 => 111001001
[1,1,1,4,1,1] => 111100011 => 111000111
[1,1,1,4,2] => 111100010 => 111000101
[1,1,1,5,1] => 111100001 => 111000011
[1,1,1,6] => 111100000 => 111000001
[1,1,2,1,1,1,1,1] => 111011111 => 110111111
[1,1,2,1,1,1,2] => 111011110 => 110111101
[1,1,2,1,1,2,1] => 111011101 => 110111011
[1,1,2,1,1,3] => 111011100 => 110111001
[1,1,2,1,2,1,1] => 111011011 => 110110111
[1,1,2,1,2,2] => 111011010 => 110110101
[1,1,2,1,3,1] => 111011001 => 110110011
[1,1,2,1,4] => 111011000 => 110110001
[1,1,2,2,1,1,1] => 111010111 => 110101111
[1,1,2,2,1,2] => 111010110 => 110101101
[1,1,2,2,2,1] => 111010101 => 110101011
[1,1,2,2,3] => 111010100 => 110101001
[1,1,2,3,1,1] => 111010011 => 110100111
[1,1,2,3,2] => 111010010 => 110100101
[1,1,2,4,1] => 111010001 => 110100011
[1,1,2,5] => 111010000 => 110100001
[1,1,3,1,1,1,1] => 111001111 => 110011111
[1,1,3,1,1,2] => 111001110 => 110011101
[1,1,3,1,2,1] => 111001101 => 110011011
[1,1,3,1,3] => 111001100 => 110011001
[1,1,3,2,1,1] => 111001011 => 110010111
[1,1,3,2,2] => 111001010 => 110010101
[1,1,3,3,1] => 111001001 => 110010011
[1,1,3,4] => 111001000 => 110010001
[1,1,4,1,1,1] => 111000111 => 110001111
[1,1,4,1,2] => 111000110 => 110001101
[1,1,4,2,1] => 111000101 => 110001011
[1,1,4,3] => 111000100 => 110001001
[1,1,5,1,1] => 111000011 => 110000111
[1,1,5,2] => 111000010 => 110000101
[1,1,6,1] => 111000001 => 110000011
[1,1,7] => 111000000 => 110000001
[1,2,1,1,1,1,1,1] => 110111111 => 101111111
[1,2,1,1,1,1,2] => 110111110 => 101111101
[1,2,1,1,1,2,1] => 110111101 => 101111011
[1,2,1,1,1,3] => 110111100 => 101111001
[1,2,1,1,2,1,1] => 110111011 => 101110111
[1,2,1,1,2,2] => 110111010 => 101110101
[1,2,1,1,3,1] => 110111001 => 101110011
[1,2,1,1,4] => 110111000 => 101110001
[1,2,1,2,1,1,1] => 110110111 => 101101111
[1,2,1,2,1,2] => 110110110 => 101101101
[1,2,1,2,2,1] => 110110101 => 101101011
[1,2,1,2,3] => 110110100 => 101101001
[1,2,1,3,1,1] => 110110011 => 101100111
[1,2,1,3,2] => 110110010 => 101100101
[1,2,1,4,1] => 110110001 => 101100011
[1,2,1,5] => 110110000 => 101100001
[1,2,2,1,1,1,1] => 110101111 => 101011111
[1,2,2,1,1,2] => 110101110 => 101011101
[1,2,2,1,2,1] => 110101101 => 101011011
[1,2,2,1,3] => 110101100 => 101011001
[1,2,2,2,1,1] => 110101011 => 101010111
[1,2,2,2,2] => 110101010 => 101010101
[1,2,2,3,1] => 110101001 => 101010011
[1,2,2,4] => 110101000 => 101010001
[1,2,3,1,1,1] => 110100111 => 101001111
[1,2,3,1,2] => 110100110 => 101001101
[1,2,3,2,1] => 110100101 => 101001011
[1,2,3,3] => 110100100 => 101001001
[1,2,4,1,1] => 110100011 => 101000111
[1,2,4,2] => 110100010 => 101000101
[1,2,5,1] => 110100001 => 101000011
[1,2,6] => 110100000 => 101000001
[1,3,1,1,1,1,1] => 110011111 => 100111111
[1,3,1,1,1,2] => 110011110 => 100111101
[1,3,1,1,2,1] => 110011101 => 100111011
[1,3,1,1,3] => 110011100 => 100111001
[1,3,1,2,1,1] => 110011011 => 100110111
[1,3,1,2,2] => 110011010 => 100110101
[1,3,1,3,1] => 110011001 => 100110011
[1,3,1,4] => 110011000 => 100110001
[1,3,2,1,1,1] => 110010111 => 100101111
[1,3,2,1,2] => 110010110 => 100101101
[1,3,2,2,1] => 110010101 => 100101011
[1,3,2,3] => 110010100 => 100101001
[1,3,3,1,1] => 110010011 => 100100111
[1,3,3,2] => 110010010 => 100100101
[1,3,4,1] => 110010001 => 100100011
[1,3,5] => 110010000 => 100100001
[1,4,1,1,1,1] => 110001111 => 100011111
[1,4,1,1,2] => 110001110 => 100011101
[1,4,1,2,1] => 110001101 => 100011011
[1,4,1,3] => 110001100 => 100011001
[1,4,2,1,1] => 110001011 => 100010111
[1,4,2,2] => 110001010 => 100010101
[1,4,3,1] => 110001001 => 100010011
[1,4,4] => 110001000 => 100010001
[1,5,1,1,1] => 110000111 => 100001111
[1,5,1,2] => 110000110 => 100001101
[1,5,2,1] => 110000101 => 100001011
[1,5,3] => 110000100 => 100001001
[1,6,1,1] => 110000011 => 100000111
[1,6,2] => 110000010 => 100000101
[1,7,1] => 110000001 => 100000011
[1,8] => 110000000 => 100000001
[2,1,1,1,1,1,1,1] => 101111111 => 011111111
[2,1,1,1,1,1,2] => 101111110 => 011111101
[2,1,1,1,1,2,1] => 101111101 => 011111011
[2,1,1,1,1,3] => 101111100 => 011111001
[2,1,1,1,2,1,1] => 101111011 => 011110111
[2,1,1,1,2,2] => 101111010 => 011110101
[2,1,1,1,3,1] => 101111001 => 011110011
[2,1,1,1,4] => 101111000 => 011110001
[2,1,1,2,1,1,1] => 101110111 => 011101111
[2,1,1,2,1,2] => 101110110 => 011101101
[2,1,1,2,2,1] => 101110101 => 011101011
[2,1,1,2,3] => 101110100 => 011101001
[2,1,1,3,1,1] => 101110011 => 011100111
[2,1,1,3,2] => 101110010 => 011100101
[2,1,1,4,1] => 101110001 => 011100011
[2,1,1,5] => 101110000 => 011100001
[2,1,2,1,1,1,1] => 101101111 => 011011111
[2,1,2,1,1,2] => 101101110 => 011011101
[2,1,2,1,2,1] => 101101101 => 011011011
[2,1,2,1,3] => 101101100 => 011011001
[2,1,2,2,1,1] => 101101011 => 011010111
[2,1,2,2,2] => 101101010 => 011010101
[2,1,2,3,1] => 101101001 => 011010011
[2,1,2,4] => 101101000 => 011010001
[2,1,3,1,1,1] => 101100111 => 011001111
[2,1,3,1,2] => 101100110 => 011001101
[2,1,3,2,1] => 101100101 => 011001011
[2,1,3,3] => 101100100 => 011001001
[2,1,4,1,1] => 101100011 => 011000111
[2,1,4,2] => 101100010 => 011000101
[2,1,5,1] => 101100001 => 011000011
[2,1,6] => 101100000 => 011000001
[2,2,1,1,1,1,1] => 101011111 => 010111111
[2,2,1,1,1,2] => 101011110 => 010111101
[2,2,1,1,2,1] => 101011101 => 010111011
[2,2,1,1,3] => 101011100 => 010111001
[2,2,1,2,1,1] => 101011011 => 010110111
[2,2,1,2,2] => 101011010 => 010110101
[2,2,1,3,1] => 101011001 => 010110011
[2,2,1,4] => 101011000 => 010110001
[2,2,2,1,1,1] => 101010111 => 010101111
[2,2,2,1,2] => 101010110 => 010101101
[2,2,2,2,1] => 101010101 => 010101011
[2,2,2,3] => 101010100 => 010101001
[2,2,3,1,1] => 101010011 => 010100111
[2,2,3,2] => 101010010 => 010100101
[2,2,4,1] => 101010001 => 010100011
[2,2,5] => 101010000 => 010100001
[2,3,1,1,1,1] => 101001111 => 010011111
[2,3,1,1,2] => 101001110 => 010011101
[2,3,1,2,1] => 101001101 => 010011011
[2,3,1,3] => 101001100 => 010011001
[2,3,2,1,1] => 101001011 => 010010111
[2,3,2,2] => 101001010 => 010010101
[2,3,3,1] => 101001001 => 010010011
[2,3,4] => 101001000 => 010010001
[2,4,1,1,1] => 101000111 => 010001111
[2,4,1,2] => 101000110 => 010001101
[2,4,2,1] => 101000101 => 010001011
[2,4,3] => 101000100 => 010001001
[2,5,1,1] => 101000011 => 010000111
[2,5,2] => 101000010 => 010000101
[2,6,1] => 101000001 => 010000011
[2,7] => 101000000 => 010000001
[3,1,1,1,1,1,1] => 100111111 => 001111111
[3,1,1,1,1,2] => 100111110 => 001111101
[3,1,1,1,2,1] => 100111101 => 001111011
[3,1,1,1,3] => 100111100 => 001111001
[3,1,1,2,1,1] => 100111011 => 001110111
[3,1,1,2,2] => 100111010 => 001110101
[3,1,1,3,1] => 100111001 => 001110011
[3,1,1,4] => 100111000 => 001110001
[3,1,2,1,1,1] => 100110111 => 001101111
[3,1,2,1,2] => 100110110 => 001101101
[3,1,2,2,1] => 100110101 => 001101011
[3,1,2,3] => 100110100 => 001101001
[3,1,3,1,1] => 100110011 => 001100111
[3,1,3,2] => 100110010 => 001100101
[3,1,4,1] => 100110001 => 001100011
[3,1,5] => 100110000 => 001100001
[3,2,1,1,1,1] => 100101111 => 001011111
[3,2,1,1,2] => 100101110 => 001011101
[3,2,1,2,1] => 100101101 => 001011011
[3,2,1,3] => 100101100 => 001011001
[3,2,2,1,1] => 100101011 => 001010111
[3,2,2,2] => 100101010 => 001010101
[3,2,3,1] => 100101001 => 001010011
[3,2,4] => 100101000 => 001010001
[3,3,1,1,1] => 100100111 => 001001111
[3,3,1,2] => 100100110 => 001001101
[3,3,2,1] => 100100101 => 001001011
[3,3,3] => 100100100 => 001001001
[3,4,1,1] => 100100011 => 001000111
[3,4,2] => 100100010 => 001000101
[3,5,1] => 100100001 => 001000011
[3,6] => 100100000 => 001000001
[4,1,1,1,1,1] => 100011111 => 000111111
[4,1,1,1,2] => 100011110 => 000111101
[4,1,1,2,1] => 100011101 => 000111011
[4,1,1,3] => 100011100 => 000111001
[4,1,2,1,1] => 100011011 => 000110111
[4,1,2,2] => 100011010 => 000110101
[4,1,3,1] => 100011001 => 000110011
[4,1,4] => 100011000 => 000110001
[4,2,1,1,1] => 100010111 => 000101111
[4,2,1,2] => 100010110 => 000101101
[4,2,2,1] => 100010101 => 000101011
[4,2,3] => 100010100 => 000101001
[4,3,1,1] => 100010011 => 000100111
[4,3,2] => 100010010 => 000100101
[4,4,1] => 100010001 => 000100011
[4,5] => 100010000 => 000100001
[5,1,1,1,1] => 100001111 => 000011111
[5,1,1,2] => 100001110 => 000011101
[5,1,2,1] => 100001101 => 000011011
[5,1,3] => 100001100 => 000011001
[5,2,1,1] => 100001011 => 000010111
[5,2,2] => 100001010 => 000010101
[5,3,1] => 100001001 => 000010011
[5,4] => 100001000 => 000010001
[6,1,1,1] => 100000111 => 000001111
[6,1,2] => 100000110 => 000001101
[6,2,1] => 100000101 => 000001011
[6,3] => 100000100 => 000001001
[7,1,1] => 100000011 => 000000111
[7,2] => 100000010 => 000000101
[8,1] => 100000001 => 000000011
[9] => 100000000 => 000000001
[1,1,1,1,1,1,1,1,1,1] => 1111111111 => 1111111111
[1,1,1,1,1,1,1,1,2] => 1111111110 => 1111111101
[1,1,1,1,1,1,1,2,1] => 1111111101 => 1111111011
[1,1,1,1,1,1,1,3] => 1111111100 => 1111111001
[1,1,1,1,1,1,2,1,1] => 1111111011 => 1111110111
[1,1,1,1,1,1,2,2] => 1111111010 => 1111110101
[1,1,1,1,1,1,3,1] => 1111111001 => 1111110011
[1,1,1,1,1,2,1,2] => 1111110110 => 1111101101
[1,1,1,1,1,2,2,1] => 1111110101 => 1111101011
[1,1,1,1,1,3,1,1] => 1111110011 => 1111100111
[1,1,1,1,1,3,2] => 1111110010 => 1111100101
[1,1,1,1,1,4,1] => 1111110001 => 1111100011
[1,1,1,1,1,5] => 1111110000 => 1111100001
[1,1,1,1,2,1,1,2] => 1111101110 => 1111011101
[1,1,1,1,2,1,2,1] => 1111101101 => 1111011011
[1,1,1,1,2,2,1,1] => 1111101011 => 1111010111
[1,1,1,1,2,2,2] => 1111101010 => 1111010101
[1,1,1,1,2,3,1] => 1111101001 => 1111010011
[1,1,1,1,2,4] => 1111101000 => 1111010001
[1,1,1,1,3,1,1,1] => 1111100111 => 1111001111
[1,1,1,1,3,3] => 1111100100 => 1111001001
[1,1,1,1,4,1,1] => 1111100011 => 1111000111
[1,1,1,1,4,2] => 1111100010 => 1111000101
[1,1,1,1,5,1] => 1111100001 => 1111000011
[1,1,1,1,6] => 1111100000 => 1111000001
[1,1,1,2,1,1,2,1] => 1111011101 => 1110111011
[1,1,1,2,1,2,1,1] => 1111011011 => 1110110111
[1,1,1,2,1,4] => 1111011000 => 1110110001
[1,1,1,2,2,1,1,1] => 1111010111 => 1110101111
[1,1,1,2,2,3] => 1111010100 => 1110101001
[1,1,1,2,3,1,1] => 1111010011 => 1110100111
[1,1,1,2,3,2] => 1111010010 => 1110100101
[1,1,1,2,4,1] => 1111010001 => 1110100011
[1,1,1,2,5] => 1111010000 => 1110100001
[1,1,1,3,1,1,1,1] => 1111001111 => 1110011111
[1,1,1,3,1,1,2] => 1111001110 => 1110011101
[1,1,1,3,1,3] => 1111001100 => 1110011001
[1,1,1,3,2,1,1] => 1111001011 => 1110010111
[1,1,1,3,2,2] => 1111001010 => 1110010101
[1,1,1,3,3,1] => 1111001001 => 1110010011
[1,1,1,3,4] => 1111001000 => 1110010001
[1,1,1,4,1,1,1] => 1111000111 => 1110001111
[1,1,1,4,2,1] => 1111000101 => 1110001011
[1,1,1,4,3] => 1111000100 => 1110001001
[1,1,1,5,1,1] => 1111000011 => 1110000111
[1,1,1,5,2] => 1111000010 => 1110000101
[1,1,1,6,1] => 1111000001 => 1110000011
[1,1,1,7] => 1111000000 => 1110000001
[1,1,2,1,1,1,1,1,1] => 1110111111 => 1101111111
[1,1,2,1,1,1,1,2] => 1110111110 => 1101111101
[1,1,2,1,1,1,2,1] => 1110111101 => 1101111011
[1,1,2,1,1,2,1,1] => 1110111011 => 1101110111
[1,1,2,1,1,4] => 1110111000 => 1101110001
[1,1,2,1,2,1,1,1] => 1110110111 => 1101101111
[1,1,2,1,2,3] => 1110110100 => 1101101001
[1,1,2,1,3,2] => 1110110010 => 1101100101
[1,1,2,1,4,1] => 1110110001 => 1101100011
[1,1,2,1,5] => 1110110000 => 1101100001
[1,1,2,2,1,3] => 1110101100 => 1101011001
[1,1,2,2,2,1,1] => 1110101011 => 1101010111
[1,1,2,2,2,2] => 1110101010 => 1101010101
[1,1,2,2,3,1] => 1110101001 => 1101010011
[1,1,2,2,4] => 1110101000 => 1101010001
[1,1,2,3,2,1] => 1110100101 => 1101001011
[1,1,2,3,3] => 1110100100 => 1101001001
[1,1,2,4,1,1] => 1110100011 => 1101000111
[1,1,2,4,2] => 1110100010 => 1101000101
[1,1,2,5,1] => 1110100001 => 1101000011
[1,1,3,1,1,1,1,1] => 1110011111 => 1100111111
[1,1,3,1,1,1,2] => 1110011110 => 1100111101
[1,1,3,1,1,3] => 1110011100 => 1100111001
[1,1,3,1,3,1] => 1110011001 => 1100110011
[1,1,3,1,4] => 1110011000 => 1100110001
[1,1,3,2,1,2] => 1110010110 => 1100101101
[1,1,3,2,2,1] => 1110010101 => 1100101011
[1,1,3,2,3] => 1110010100 => 1100101001
[1,1,3,3,1,1] => 1110010011 => 1100100111
[1,1,3,3,2] => 1110010010 => 1100100101
[1,1,3,4,1] => 1110010001 => 1100100011
[1,1,3,5] => 1110010000 => 1100100001
[1,1,4,1,2,1] => 1110001101 => 1100011011
[1,1,4,1,3] => 1110001100 => 1100011001
[1,1,4,2,1,1] => 1110001011 => 1100010111
[1,1,4,2,2] => 1110001010 => 1100010101
[1,1,4,3,1] => 1110001001 => 1100010011
[1,1,5,1,1,1] => 1110000111 => 1100001111
[1,1,5,2,1] => 1110000101 => 1100001011
[1,1,5,3] => 1110000100 => 1100001001
[1,1,6,1,1] => 1110000011 => 1100000111
[1,1,6,2] => 1110000010 => 1100000101
[1,1,7,1] => 1110000001 => 1100000011
[1,2,1,1,1,1,1,1,1] => 1101111111 => 1011111111
[1,2,1,1,1,1,1,2] => 1101111110 => 1011111101
[1,2,1,1,1,1,2,1] => 1101111101 => 1011111011
[1,2,1,1,1,2,1,1] => 1101111011 => 1011110111
[1,2,1,1,1,3,1] => 1101111001 => 1011110011
[1,2,1,1,2,1,1,1] => 1101110111 => 1011101111
[1,2,1,1,4,1] => 1101110001 => 1011100011
[1,2,1,1,5] => 1101110000 => 1011100001
[1,2,1,2,1,1,1,1] => 1101101111 => 1011011111
[1,2,1,2,2,1,1] => 1101101011 => 1011010111
[1,2,1,2,3,1] => 1101101001 => 1011010011
[1,2,1,2,4] => 1101101000 => 1011010001
[1,2,1,3,2,1] => 1101100101 => 1011001011
[1,2,1,3,3] => 1101100100 => 1011001001
[1,2,1,4,1,1] => 1101100011 => 1011000111
[1,2,1,4,2] => 1101100010 => 1011000101
[1,2,1,5,1] => 1101100001 => 1011000011
[1,2,2,1,1,1,1,1] => 1101011111 => 1010111111
[1,2,2,1,2,1,1] => 1101011011 => 1010110111
[1,2,2,1,3,1] => 1101011001 => 1010110011
[1,2,2,1,4] => 1101011000 => 1010110001
[1,2,2,2,1,1,1] => 1101010111 => 1010101111
[1,2,2,2,2,1] => 1101010101 => 1010101011
[1,2,2,2,3] => 1101010100 => 1010101001
[1,2,2,3,1,1] => 1101010011 => 1010100111
[1,2,2,3,2] => 1101010010 => 1010100101
[1,2,2,4,1] => 1101010001 => 1010100011
[1,2,3,1,1,1,1] => 1101001111 => 1010011111
[1,2,3,1,1,2] => 1101001110 => 1010011101
[1,2,3,1,2,1] => 1101001101 => 1010011011
[1,2,3,1,3] => 1101001100 => 1010011001
[1,2,3,2,1,1] => 1101001011 => 1010010111
[1,2,3,2,2] => 1101001010 => 1010010101
[1,2,3,3,1] => 1101001001 => 1010010011
[1,2,4,1,1,1] => 1101000111 => 1010001111
[1,2,4,2,1] => 1101000101 => 1010001011
[1,2,5,1,1] => 1101000011 => 1010000111
[1,2,5,2] => 1101000010 => 1010000101
[1,2,6,1] => 1101000001 => 1010000011
[1,3,1,1,1,1,1,1] => 1100111111 => 1001111111
[1,3,1,1,1,3] => 1100111100 => 1001111001
[1,3,1,1,3,1] => 1100111001 => 1001110011
[1,3,1,1,4] => 1100111000 => 1001110001
[1,3,1,2,2,1] => 1100110101 => 1001101011
[1,3,1,2,3] => 1100110100 => 1001101001
[1,3,1,3,1,1] => 1100110011 => 1001100111
[1,3,1,3,2] => 1100110010 => 1001100101
[1,3,1,4,1] => 1100110001 => 1001100011
[1,3,1,5] => 1100110000 => 1001100001
[1,3,2,1,1,2] => 1100101110 => 1001011101
[1,3,2,1,2,1] => 1100101101 => 1001011011
[1,3,2,1,3] => 1100101100 => 1001011001
[1,3,2,2,1,1] => 1100101011 => 1001010111
[1,3,2,2,2] => 1100101010 => 1001010101
[1,3,2,3,1] => 1100101001 => 1001010011
[1,3,3,1,1,1] => 1100100111 => 1001001111
[1,3,3,1,2] => 1100100110 => 1001001101
[1,3,3,2,1] => 1100100101 => 1001001011
[1,3,3,3] => 1100100100 => 1001001001
[1,3,4,1,1] => 1100100011 => 1001000111
[1,3,5,1] => 1100100001 => 1001000011
[1,4,1,1,1,2] => 1100011110 => 1000111101
[1,4,1,1,2,1] => 1100011101 => 1000111011
[1,4,1,1,3] => 1100011100 => 1000111001
[1,4,1,2,1,1] => 1100011011 => 1000110111
[1,4,1,3,1] => 1100011001 => 1000110011
[1,4,2,1,1,1] => 1100010111 => 1000101111
[1,4,2,2,1] => 1100010101 => 1000101011
[1,4,3,1,1] => 1100010011 => 1000100111
[1,4,3,2] => 1100010010 => 1000100101
[1,5,1,1,1,1] => 1100001111 => 1000011111
[1,5,1,2,1] => 1100001101 => 1000011011
[1,5,1,3] => 1100001100 => 1000011001
[1,5,2,1,1] => 1100001011 => 1000010111
[1,5,2,2] => 1100001010 => 1000010101
[1,5,4] => 1100001000 => 1000010001
[1,6,1,1,1] => 1100000111 => 1000001111
[1,6,1,2] => 1100000110 => 1000001101
[1,7,1,1] => 1100000011 => 1000000111
[1,7,2] => 1100000010 => 1000000101
[1,8,1] => 1100000001 => 1000000011
[1,9] => 1100000000 => 1000000001
[2,1,1,1,1,1,1,1,1] => 1011111111 => 0111111111
[2,1,1,1,1,1,1,2] => 1011111110 => 0111111101
[2,1,1,1,1,1,2,1] => 1011111101 => 0111111011
[2,1,1,1,1,2,1,1] => 1011111011 => 0111110111
[2,1,1,1,2,1,1,1] => 1011110111 => 0111101111
[2,1,1,1,2,3] => 1011110100 => 0111101001
[2,1,1,1,4,1] => 1011110001 => 0111100011
[2,1,1,1,5] => 1011110000 => 0111100001
[2,1,1,2,2,1,1] => 1011101011 => 0111010111
[2,1,1,2,3,1] => 1011101001 => 0111010011
[2,1,1,2,4] => 1011101000 => 0111010001
[2,1,1,3,2,1] => 1011100101 => 0111001011
[2,1,1,3,3] => 1011100100 => 0111001001
[2,1,1,4,1,1] => 1011100011 => 0111000111
[2,1,1,4,2] => 1011100010 => 0111000101
[2,1,1,5,1] => 1011100001 => 0111000011
[2,1,1,6] => 1011100000 => 0111000001
[2,1,2,1,1,1,1,1] => 1011011111 => 0110111111
[2,1,2,1,1,3] => 1011011100 => 0110111001
[2,1,2,1,3,1] => 1011011001 => 0110110011
[2,1,2,1,4] => 1011011000 => 0110110001
[2,1,2,2,1,1,1] => 1011010111 => 0110101111
[2,1,2,2,2,1] => 1011010101 => 0110101011
[2,1,2,2,3] => 1011010100 => 0110101001
[2,1,2,3,1,1] => 1011010011 => 0110100111
[2,1,2,3,2] => 1011010010 => 0110100101
[2,1,2,4,1] => 1011010001 => 0110100011
[2,1,2,5] => 1011010000 => 0110100001
[2,1,3,1,2,1] => 1011001101 => 0110011011
[2,1,3,1,3] => 1011001100 => 0110011001
[2,1,3,2,1,1] => 1011001011 => 0110010111
[2,1,3,2,2] => 1011001010 => 0110010101
[2,1,3,3,1] => 1011001001 => 0110010011
[2,1,3,4] => 1011001000 => 0110010001
[2,1,4,1,1,1] => 1011000111 => 0110001111
[2,1,4,2,1] => 1011000101 => 0110001011
[2,1,4,3] => 1011000100 => 0110001001
[2,1,5,1,1] => 1011000011 => 0110000111
[2,1,5,2] => 1011000010 => 0110000101
[2,1,6,1] => 1011000001 => 0110000011
[2,2,1,1,1,1,1,1] => 1010111111 => 0101111111
[2,2,1,1,1,1,2] => 1010111110 => 0101111101
[2,2,1,1,3,1] => 1010111001 => 0101110011
[2,2,1,1,4] => 1010111000 => 0101110001
[2,2,1,2,1,1,1] => 1010110111 => 0101101111
[2,2,1,2,2,1] => 1010110101 => 0101101011
[2,2,1,2,3] => 1010110100 => 0101101001
[2,2,1,3,1,1] => 1010110011 => 0101100111
[2,2,1,3,2] => 1010110010 => 0101100101
[2,2,1,4,1] => 1010110001 => 0101100011
[2,2,1,5] => 1010110000 => 0101100001
[2,2,2,1,1,1,1] => 1010101111 => 0101011111
[2,2,2,1,2,1] => 1010101101 => 0101011011
[2,2,2,1,3] => 1010101100 => 0101011001
[2,2,2,2,1,1] => 1010101011 => 0101010111
[2,2,2,2,2] => 1010101010 => 0101010101
[2,2,2,3,1] => 1010101001 => 0101010011
[2,2,2,4] => 1010101000 => 0101010001
[2,2,3,1,1,1] => 1010100111 => 0101001111
[2,2,3,1,2] => 1010100110 => 0101001101
[2,2,3,2,1] => 1010100101 => 0101001011
[2,2,3,3] => 1010100100 => 0101001001
[2,2,4,1,1] => 1010100011 => 0101000111
[2,2,4,2] => 1010100010 => 0101000101
[2,3,1,1,2,1] => 1010011101 => 0100111011
[2,3,1,2,1,1] => 1010011011 => 0100110111
[2,3,1,2,2] => 1010011010 => 0100110101
[2,3,1,3,1] => 1010011001 => 0100110011
[2,3,1,4] => 1010011000 => 0100110001
[2,3,2,1,1,1] => 1010010111 => 0100101111
[2,3,2,1,2] => 1010010110 => 0100101101
[2,3,2,2,1] => 1010010101 => 0100101011
[2,3,2,3] => 1010010100 => 0100101001
[2,3,3,1,1] => 1010010011 => 0100100111
[2,3,3,2] => 1010010010 => 0100100101
[2,3,4,1] => 1010010001 => 0100100011
[2,4,1,1,1,1] => 1010001111 => 0100011111
[2,4,1,1,2] => 1010001110 => 0100011101
[2,4,1,2,1] => 1010001101 => 0100011011
[2,4,1,3] => 1010001100 => 0100011001
[2,4,2,1,1] => 1010001011 => 0100010111
[2,4,2,2] => 1010001010 => 0100010101
[2,5,1,1,1] => 1010000111 => 0100001111
[2,5,2,1] => 1010000101 => 0100001011
[2,6,2] => 1010000010 => 0100000101
[2,7,1] => 1010000001 => 0100000011
[3,1,1,1,1,1,1,1] => 1001111111 => 0011111111
[3,1,1,1,1,1,2] => 1001111110 => 0011111101
[3,1,1,1,1,3] => 1001111100 => 0011111001
[3,1,1,1,3,1] => 1001111001 => 0011110011
[3,1,1,1,4] => 1001111000 => 0011110001
[3,1,1,2,2,1] => 1001110101 => 0011101011
[3,1,1,2,3] => 1001110100 => 0011101001
[3,1,1,3,1,1] => 1001110011 => 0011100111
[3,1,1,4,1] => 1001110001 => 0011100011
[3,1,1,5] => 1001110000 => 0011100001
[3,1,2,1,2,1] => 1001101101 => 0011011011
[3,1,2,1,3] => 1001101100 => 0011011001
[3,1,2,2,1,1] => 1001101011 => 0011010111
[3,1,2,2,2] => 1001101010 => 0011010101
[3,1,2,3,1] => 1001101001 => 0011010011
[3,1,2,4] => 1001101000 => 0011010001
[3,1,3,1,1,1] => 1001100111 => 0011001111
[3,1,3,1,2] => 1001100110 => 0011001101
[3,1,3,2,1] => 1001100101 => 0011001011
[3,1,3,3] => 1001100100 => 0011001001
[3,1,4,2] => 1001100010 => 0011000101
[3,1,5,1] => 1001100001 => 0011000011
[3,2,1,1,1,1,1] => 1001011111 => 0010111111
[3,2,1,1,1,2] => 1001011110 => 0010111101
[3,2,1,1,2,1] => 1001011101 => 0010111011
[3,2,1,2,1,1] => 1001011011 => 0010110111
[3,2,1,2,2] => 1001011010 => 0010110101
[3,2,1,3,1] => 1001011001 => 0010110011
[3,2,1,4] => 1001011000 => 0010110001
[3,2,2,1,1,1] => 1001010111 => 0010101111
[3,2,2,1,2] => 1001010110 => 0010101101
[3,2,2,2,1] => 1001010101 => 0010101011
[3,2,2,3] => 1001010100 => 0010101001
[3,2,3,2] => 1001010010 => 0010100101
[3,3,1,1,1,1] => 1001001111 => 0010011111
[3,3,1,1,2] => 1001001110 => 0010011101
[3,3,1,2,1] => 1001001101 => 0010011011
[3,3,1,3] => 1001001100 => 0010011001
[3,3,2,1,1] => 1001001011 => 0010010111
[3,3,2,2] => 1001001010 => 0010010101
[3,4,1,1,1] => 1001000111 => 0010001111
[3,4,1,2] => 1001000110 => 0010001101
[3,7] => 1001000000 => 0010000001
[4,1,1,1,1,1,1] => 1000111111 => 0001111111
[4,1,1,1,1,2] => 1000111110 => 0001111101
[4,1,1,1,2,1] => 1000111101 => 0001111011
[4,1,1,1,3] => 1000111100 => 0001111001
[4,1,1,2,1,1] => 1000111011 => 0001110111
[4,1,1,2,2] => 1000111010 => 0001110101
[4,1,1,4] => 1000111000 => 0001110001
[4,1,2,1,1,1] => 1000110111 => 0001101111
[4,1,2,1,2] => 1000110110 => 0001101101
[4,1,2,2,1] => 1000110101 => 0001101011
[4,1,2,3] => 1000110100 => 0001101001
[4,1,3,1,1] => 1000110011 => 0001100111
[4,1,3,2] => 1000110010 => 0001100101
[4,1,4,1] => 1000110001 => 0001100011
[4,2,1,1,1,1] => 1000101111 => 0001011111
[4,2,1,1,2] => 1000101110 => 0001011101
[4,2,1,3] => 1000101100 => 0001011001
[4,2,2,1,1] => 1000101011 => 0001010111
[4,2,2,2] => 1000101010 => 0001010101
[4,3,2,1] => 1000100101 => 0001001011
[5,1,1,1,1,1] => 1000011111 => 0000111111
[5,1,1,1,2] => 1000011110 => 0000111101
[5,1,1,2,1] => 1000011101 => 0000111011
[5,1,1,3] => 1000011100 => 0000111001
[5,1,2,1,1] => 1000011011 => 0000110111
[5,1,3,1] => 1000011001 => 0000110011
[5,2,1,1,1] => 1000010111 => 0000101111
[5,2,1,2] => 1000010110 => 0000101101
[5,2,2,1] => 1000010101 => 0000101011
[5,5] => 1000010000 => 0000100001
[6,1,1,1,1] => 1000001111 => 0000011111
[6,1,1,2] => 1000001110 => 0000011101
[6,1,2,1] => 1000001101 => 0000011011
[6,2,1,1] => 1000001011 => 0000010111
[6,2,2] => 1000001010 => 0000010101
[6,3,1] => 1000001001 => 0000010011
[7,1,1,1] => 1000000111 => 0000001111
[7,1,2] => 1000000110 => 0000001101
[7,2,1] => 1000000101 => 0000001011
[7,3] => 1000000100 => 0000001001
[8,1,1] => 1000000011 => 0000000111
[8,2] => 1000000010 => 0000000101
[9,1] => 1000000001 => 0000000011
[10] => 1000000000 => 0000000001
[1,10] => 11000000000 => 10000000001
[1,8,1,1] => 11000000011 => 10000000111
[1,1,8,1] => 11100000001 => 11000000011
[10,1] => 10000000001 => 00000000011
[1,1,1,1,1,1,1,1,1,1,1,1] => 111111111111 => 111111111111
[1,1,1,1,1,1,3,3] => 111111100100 => 111111001001
[1,1,1,1,2,1,2,3] => 111110110100 => 111101101001
[1,1,1,1,3,1,1,3] => 111110011100 => 111100111001
[1,1,1,1,4,4] => 111110001000 => 111100010001
[1,1,2,2,3,3] => 111010100100 => 110101001001
[1,1,2,1,1,1,2,3] => 111011110100 => 110111101001
[1,1,2,1,2,1,1,3] => 111011011100 => 110110111001
[1,1,2,1,3,4] => 111011001000 => 110110010001
[1,1,3,3,2,2] => 111001001010 => 110010010101
[1,1,3,2,2,3] => 111001010100 => 110010101001
[1,1,3,1,1,1,1,3] => 111001111100 => 110011111001
[1,1,3,1,2,4] => 111001101000 => 110011010001
[1,1,4,4,1,1] => 111000100011 => 110001000111
[1,1,4,2,1,3] => 111000101100 => 110001011001
[1,1,4,1,1,4] => 111000111000 => 110001110001
[1,1,5,5] => 111000010000 => 110000100001
[2,2,1,1,3,3] => 101011100100 => 010111001001
[2,2,2,2,2,2] => 101010101010 => 010101010101
[2,2,2,1,2,3] => 101010110100 => 010101101001
[2,2,3,3,1,1] => 101010010011 => 010100100111
[2,2,3,2,1,2] => 101010010110 => 010100101101
[2,1,1,2,3,3] => 101110100100 => 011101001001
[2,1,1,1,1,1,2,3] => 101111110100 => 011111101001
[2,1,1,1,2,1,1,3] => 101111011100 => 011110111001
[2,1,1,1,3,4] => 101111001000 => 011110010001
[2,1,2,3,1,1,1,1] => 101101001111 => 011010011111
[2,1,2,3,2,2] => 101101001010 => 011010010101
[2,1,2,2,2,3] => 101101010100 => 011010101001
[2,1,2,1,1,3,1,1] => 101101110011 => 011011100111
[2,1,2,1,1,1,1,3] => 101101111100 => 011011111001
[2,1,2,1,2,4] => 101101101000 => 011011010001
[2,1,3,4,1,1] => 101100100011 => 011001000111
[2,1,3,2,1,3] => 101100101100 => 011001011001
[2,1,3,1,1,4] => 101100111000 => 011001110001
[2,1,4,5] => 101100010000 => 011000100001
[3,3,1,1,2,2] => 100100111010 => 001001110101
[3,3,2,2,1,1] => 100100101011 => 001001010111
[3,3,2,1,1,2] => 100100101110 => 001001011101
[3,3,3,3] => 100100100100 => 001001001001
[3,2,1,2,1,1,1,1] => 100101101111 => 001011011111
[3,2,1,2,2,2] => 100101101010 => 001011010101
[3,2,1,1,1,2,1,1] => 100101111011 => 001011110111
[3,2,1,1,2,3] => 100101110100 => 001011101001
[3,2,2,2,1,2] => 100101010110 => 001010101101
[3,1,1,2,2,3] => 100111010100 => 001110101001
[3,1,1,1,1,1,1,3] => 100111111100 => 001111111001
[3,1,1,1,2,4] => 100111101000 => 001111010001
[3,1,2,4,1,1] => 100110100011 => 001101000111
[3,1,2,3,1,2] => 100110100110 => 001101001101
[3,1,3,5] => 100110010000 => 001100100001
[4,4,1,1,1,1] => 100010001111 => 000100011111
[4,3,1,2,1,1] => 100010011011 => 000100110111
[4,3,1,1,1,2] => 100010011110 => 000100111101
[4,3,2,3] => 100010010100 => 000100101001
[4,2,1,2,1,2] => 100010110110 => 000101101101
[4,1,1,3,1,2] => 100011100110 => 000111001101
[4,1,1,2,1,3] => 100011101100 => 000111011001
[4,1,1,1,1,4] => 100011111000 => 000111110001
[4,1,2,5] => 100011010000 => 000110100001
[5,3,1,3] => 100001001100 => 000010011001
[5,1,1,5] => 100001110000 => 000011100001
[1,2,2,2,2,2,1] => 110101010101 => 101010101011
[1,2,2,2,3,2] => 110101010010 => 101010100101
[1,2,2,3,3,1] => 110101001001 => 101010010011
[1,2,2,3,2,2] => 110101001010 => 101010010101
[1,2,3,3,2,1] => 110100100101 => 101001001011
[1,2,3,2,3,1] => 110100101001 => 101001010011
[1,2,3,2,2,2] => 110100101010 => 101001010101
[1,3,3,2,2,1] => 110010010101 => 100100101011
[1,3,5,3] => 110010000100 => 100100001001
[1,3,2,3,2,1] => 110010100101 => 100101001011
[1,3,2,2,3,1] => 110010101001 => 100101010011
[1,3,2,2,2,2] => 110010101010 => 100101010101
[1,5,5,1] => 110000100001 => 100001000011
[1,5,3,3] => 110000100100 => 100001001001
[2,3,2,2,2,1] => 101001010101 => 010010101011
[2,3,4,3] => 101001000100 => 010010001001
[2,5,4,1] => 101000010001 => 010000100011
[2,5,2,3] => 101000010100 => 010000101001
[2,2,3,2,2,1] => 101010010101 => 010100101011
[2,2,2,3,2,1] => 101010100101 => 010101001011
[2,2,2,2,3,1] => 101010101001 => 010101010011
[2,4,5,1] => 101000100001 => 010001000011
[3,4,4,1] => 100100010001 => 001000100011
[3,3,5,1] => 100100100001 => 001001000011
[4,5,2,1] => 100010000101 => 000100001011
[4,3,4,1] => 100010010001 => 000100100011
[1,8,2] => 11000000010 => 10000000101
[1,7,1,2] => 11000000110 => 10000001101
[1,6,1,1,2] => 11000001110 => 10000011101
[1,5,1,1,1,2] => 11000011110 => 10000111101
[1,4,1,1,1,1,2] => 11000111110 => 10001111101
[1,3,1,1,1,1,1,2] => 11001111110 => 10011111101
[1,2,1,1,1,1,1,1,2] => 11011111110 => 10111111101
[1,1,1,1,1,1,1,1,1,2] => 11111111110 => 11111111101
[1,11] => 110000000000 => 100000000001
[1,4,2,1,1,2] => 11000101110 => 10001011101
[1,2,2,2,2,2] => 11010101010 => 10101010101
[1,2,2,2,1,3] => 11010101100 => 10101011001
[1,2,2,1,2,3] => 11010110100 => 10101101001
[1,2,1,2,2,3] => 11011010100 => 10110101001
[1,2,1,1,4,2] => 11011100010 => 10111000101
[1,2,1,1,2,4] => 11011101000 => 10111010001
[1,1,2,2,2,3] => 11101010100 => 11010101001
[1,1,1,2,4,2] => 11110100010 => 11101000101
[1,1,1,1,5,2] => 11111000010 => 11110000101
[1,1,1,1,1,6] => 11111100000 => 11111000001
[1,1,2,1,4,2,1] => 111011000101 => 110110001011
[1,1,2,3,2,2,1] => 111010010101 => 110100101011
[3,1,2,1,2,2,1] => 100110110101 => 001101101011
[1,3,2,1,2,2,1] => 110010110101 => 100101101011
[1,1,4,1,2,2,1] => 111000110101 => 110001101011
[1,1,2,1,2,4,1] => 111011010001 => 110110100011
[3,1,2,5,1] => 100110100001 => 001101000011
[1,1,1,2,1,5,1] => 111101100001 => 111011000011
[1,2,2,1,2,3,1] => 110101101001 => 101011010011
[1,1,2,2,2,3,1] => 111010101001 => 110101010011
[1,1,1,2,3,3,1] => 111101001001 => 111010010011
[1,3,1,2,1,3,1] => 110011011001 => 100110110011
[1,1,3,2,1,3,1] => 111001011001 => 110010110011
[1,1,1,4,1,3,1] => 111100011001 => 111000110011
[1,2,4,1,2,1,1] => 110100011011 => 101000110111
[3,2,2,1,2,1,1] => 100101011011 => 001010110111
[1,4,2,1,2,1,1] => 110001011011 => 100010110111
[1,2,2,3,2,1,1] => 110101001011 => 101010010111
[1,1,2,4,2,1,1] => 111010001011 => 110100010111
[3,1,2,2,2,1,1] => 100110101011 => 001101010111
[1,3,2,2,2,1,1] => 110010101011 => 100101010111
[1,1,4,2,2,1,1] => 111000101011 => 110001010111
[1,2,2,1,4,1,1] => 110101100011 => 101011000111
[3,3,4,1,1] => 100100100011 => 001001000111
[1,1,2,2,4,1,1] => 111010100011 => 110101000111
[1,1,1,2,5,1,1] => 111101000011 => 111010000111
[3,1,1,2,3,1,1] => 100111010011 => 001110100111
[1,3,1,2,3,1,1] => 110011010011 => 100110100111
[1,1,3,2,3,1,1] => 111001010011 => 110010100111
[1,1,1,4,3,1,1] => 111100010011 => 111000100111
[5,1,1,2,1,1,1] => 100001110111 => 000011101111
[3,3,1,2,1,1,1] => 100100110111 => 001001101111
[1,5,1,2,1,1,1] => 110000110111 => 100001101111
[3,1,3,2,1,1,1] => 100110010111 => 001100101111
[1,3,3,2,1,1,1] => 110010010111 => 100100101111
[3,1,1,4,1,1,1] => 100111000111 => 001110001111
[1,3,1,4,1,1,1] => 110011000111 => 100110001111
[1,1,3,4,1,1,1] => 111001000111 => 110010001111
[1,1,1,6,1,1,1] => 111100000111 => 111000001111
[2,2,2,2,1,2,1] => 101010101101 => 010101011011
[2,2,2,1,2,2,1] => 101010110101 => 010101101011
[2,2,1,2,1,1,2,1] => 101011011101 => 010110111011
[2,2,1,2,2,2,1] => 101011010101 => 010110101011
[2,2,1,1,1,2,2,1] => 101011110101 => 010111101011
[2,1,2,1,2,1,2,1] => 101101101101 => 011011011011
[2,1,2,1,1,2,2,1] => 101101110101 => 011011101011
[2,1,2,2,1,1,2,1] => 101101011101 => 011010111011
[2,1,2,2,2,2,1] => 101101010101 => 011010101011
[2,1,1,2,1,2,2,1] => 101110110101 => 011101101011
[2,1,1,1,2,2,2,1] => 101111010101 => 011110101011
[1,2,1,2,2,1,2,1] => 110110101101 => 101101011011
[1,2,1,1,2,2,2,1] => 110111010101 => 101110101011
[1,2,2,1,1,2,2,1] => 110101110101 => 101011101011
[1,2,2,2,1,1,2,1] => 110101011101 => 101010111011
[1,1,2,2,1,2,2,1] => 111010110101 => 110101101011
[1,1,1,2,2,2,2,1] => 111101010101 => 111010101011
[3,3,3,2] => 10010010010 => 00100100101
[3,4,4] => 10010001000 => 00100010001
[2,3,3,3] => 10100100100 => 01001001001
[4,4,3] => 10001000100 => 00010001001
[2,1,1,1,1,1,1,1,1,1] => 10111111111 => 01111111111
[3,2,2,2,2,1] => 100101010101 => 001010101011
[7,5] => 100000010000 => 000000100001
[2,1,1,1,1,1,1,2,1] => 10111111101 => 01111111011
[11,1] => 100000000001 => 000000000011
[2,1,8,1] => 101100000001 => 011000000011
[2,1,1,1,6,1] => 101111000001 => 011110000011
[2,1,1,1,1,5,1] => 101111100001 => 011111000011
[2,1,1,1,1,1,4,1] => 101111110001 => 011111100011
[2,1,1,1,1,1,1,1,2,1] => 101111111101 => 011111111011
[2,2,2,2,2,1] => 10101010101 => 01010101011
[5,2,1,1,1,1] => 10000101111 => 00001011111
[6,1,1,1,1,1] => 10000011111 => 00000111111
[2,2,1,1,1,2,1,1,1] => 101011110111 => 010111101111
[2,1,2,1,1,1,2,1,1] => 101101111011 => 011011110111
[2,1,2,1,1,2,1,1,1] => 101101110111 => 011011101111
[2,1,1,2,1,1,2,1,1] => 101110111011 => 011101110111
[2,1,1,2,1,2,1,1,1] => 101110110111 => 011101101111
[1,2,1,1,1,1,2,1,1,1] => 110111110111 => 101111101111
[1,2,2,1,2,2,1,1] => 110101101011 => 101011010111
[1,2,1,1,1,2,1,1,1,1] => 110111101111 => 101111011111
[1,1,2,1,1,1,2,1,1,1] => 111011110111 => 110111101111
[1,1,1,2,1,1,1,1,2,1] => 111101111101 => 111011111011
[1,1,1,2,1,1,1,2,1,1] => 111101111011 => 111011110111
[1,1,1,2,1,1,2,1,1,1] => 111101110111 => 111011101111
[1,1,1,2,1,2,1,1,1,1] => 111101101111 => 111011011111
[1,1,1,1,2,1,1,1,2,1] => 111110111101 => 111101111011
[1,1,1,1,2,1,2,1,1,1] => 111110110111 => 111101101111
[2,1,1,1,2,1,1,2] => 10111101110 => 01111011101
[2,1,1,2,1,1,1,2] => 10111011110 => 01110111101
[2,2,1,1,1,1,1,2] => 10101111110 => 01011111101
[3,1,1,1,1,1,1,2] => 10011111110 => 00111111101
[1,2,2,4,2,1] => 110101000101 => 101010001011
[1,2,4,2,2,1] => 110100010101 => 101000101011
[1,4,2,2,2,1] => 110001010101 => 100010101011
[2,2,2,2,2,1,1] => 101010101011 => 010101010111
[2,2,1,2,2,1,1,1] => 101011010111 => 010110101111
[2,1,2,2,2,1,1,1] => 101101010111 => 011010101111
[1,2,2,2,2,1,1,1] => 110101010111 => 101010101111
[1,2,1,1,2,1,1,1,1,1] => 110111011111 => 101110111111
[1,1,2,1,2,1,1,1,1,1] => 111011011111 => 110110111111
[1,1,1,2,2,1,1,1,1,1] => 111101011111 => 111010111111
[9,2] => 10000000010 => 00000000101
[1,9,1] => 11000000001 => 10000000011
[1,1,1,1,1,1,1,2,2,1] => 111111110101 => 111111101011
[1,1,1,1,1,2,2,1,1,1] => 111111010111 => 111110101111
[1,1,1,1,1,2,1,1,2,1] => 111111011101 => 111110111011
[1,2,2,1,1,1,1,1,1,1] => 110101111111 => 101011111111
[1,2,1,1,1,1,1,1,2,1] => 110111111101 => 101111111011
[1,2,2,2,3,1,1] => 110101010011 => 101010100111
[1,2,2,3,1,2,1] => 110101001101 => 101010011011
[1,2,2,4,1,1,1] => 110101000111 => 101010001111
[1,2,3,1,2,2,1] => 110100110101 => 101001101011
[1,2,3,1,3,1,1] => 110100110011 => 101001100111
[1,2,3,2,1,2,1] => 110100101101 => 101001011011
[1,2,4,1,1,2,1] => 110100011101 => 101000111011
[1,2,3,2,2,1,1] => 110100101011 => 101001010111
[1,2,3,3,1,1,1] => 110100100111 => 101001001111
[1,2,4,2,1,1,1] => 110100010111 => 101000101111
[1,2,5,1,1,1,1] => 110100001111 => 101000011111
[1,3,1,2,2,2,1] => 110011010101 => 100110101011
[1,3,1,3,1,2,1] => 110011001101 => 100110011011
[1,3,1,3,2,1,1] => 110011001011 => 100110010111
[1,3,2,1,3,1,1] => 110010110011 => 100101100111
[1,4,1,1,2,2,1] => 110001110101 => 100011101011
[1,4,1,1,3,1,1] => 110001110011 => 100011100111
[1,3,2,2,1,2,1] => 110010101101 => 100101011011
[1,3,3,1,1,2,1] => 110010011101 => 100100111011
[1,4,1,2,1,2,1] => 110001101101 => 100011011011
[1,4,2,1,1,2,1] => 110001011101 => 100010111011
[1,5,1,1,1,2,1] => 110000111101 => 100001111011
[1,3,2,3,1,1,1] => 110010100111 => 100101001111
[1,3,3,1,2,1,1] => 110010011011 => 100100110111
[1,3,4,1,1,1,1] => 110010001111 => 100100011111
[1,4,1,2,2,1,1] => 110001101011 => 100011010111
[1,4,1,3,1,1,1] => 110001100111 => 100011001111
[1,5,1,1,2,1,1] => 110000111011 => 100001110111
[1,4,2,2,1,1,1] => 110001010111 => 100010101111
[1,4,3,1,1,1,1] => 110001001111 => 100010011111
[1,5,2,1,1,1,1] => 110000101111 => 100001011111
[1,6,1,1,1,1,1] => 110000011111 => 100000111111
[2,1,2,2,3,1,1] => 101101010011 => 011010100111
[2,1,2,3,1,2,1] => 101101001101 => 011010011011
[2,1,2,3,2,1,1] => 101101001011 => 011010010111
[2,1,2,4,1,1,1] => 101101000111 => 011010001111
[2,1,3,1,2,2,1] => 101100110101 => 011001101011
[2,1,3,1,3,1,1] => 101100110011 => 011001100111
[2,1,3,2,1,2,1] => 101100101101 => 011001011011
[2,1,4,1,1,2,1] => 101100011101 => 011000111011
[2,1,3,2,2,1,1] => 101100101011 => 011001010111
[2,1,3,3,1,1,1] => 101100100111 => 011001001111
[2,1,4,1,2,1,1] => 101100011011 => 011000110111
[2,1,4,2,1,1,1] => 101100010111 => 011000101111
[2,1,5,1,1,1,1] => 101100001111 => 011000011111
[2,2,1,2,3,1,1] => 101011010011 => 010110100111
[2,2,1,3,1,2,1] => 101011001101 => 010110011011
[2,2,1,3,2,1,1] => 101011001011 => 010110010111
[2,2,1,4,1,1,1] => 101011000111 => 010110001111
[3,1,1,2,2,2,1] => 100111010101 => 001110101011
[3,1,1,3,1,2,1] => 100111001101 => 001110011011
[3,1,1,3,2,1,1] => 100111001011 => 001110010111
[2,2,2,1,3,1,1] => 101010110011 => 010101100111
[2,3,1,1,2,2,1] => 101001110101 => 010011101011
[2,3,1,1,3,1,1] => 101001110011 => 010011100111
[3,1,2,1,3,1,1] => 100110110011 => 001101100111
[3,2,1,1,2,2,1] => 100101110101 => 001011101011
[3,2,1,1,3,1,1] => 100101110011 => 001011100111
[4,1,1,1,2,2,1] => 100011110101 => 000111101011
[4,1,1,1,3,1,1] => 100011110011 => 000111100111
[2,2,3,1,1,2,1] => 101010011101 => 010100111011
[2,3,1,2,1,2,1] => 101001101101 => 010011011011
[2,3,2,1,1,2,1] => 101001011101 => 010010111011
[2,4,1,1,1,2,1] => 101000111101 => 010001111011
[3,1,2,2,1,2,1] => 100110101101 => 001101011011
[3,1,3,1,1,2,1] => 100110011101 => 001100111011
[3,2,1,2,1,2,1] => 100101101101 => 001011011011
[4,1,1,2,1,2,1] => 100011101101 => 000111011011
[3,2,2,1,1,2,1] => 100101011101 => 001010111011
[3,3,1,1,1,2,1] => 100100111101 => 001001111011
[4,1,2,1,1,2,1] => 100011011101 => 000110111011
[4,2,1,1,1,2,1] => 100010111101 => 000101111011
[5,1,1,1,1,2,1] => 100001111101 => 000011111011
[2,2,2,3,1,1,1] => 101010100111 => 010101001111
[2,2,3,1,2,1,1] => 101010011011 => 010100110111
[2,2,3,2,1,1,1] => 101010010111 => 010100101111
[2,2,4,1,1,1,1] => 101010001111 => 010100011111
[2,3,1,2,2,1,1] => 101001101011 => 010011010111
[2,3,1,3,1,1,1] => 101001100111 => 010011001111
[2,3,2,1,2,1,1] => 101001011011 => 010010110111
[2,4,1,1,2,1,1] => 101000111011 => 010001110111
[2,3,2,2,1,1,1] => 101001010111 => 010010101111
[2,3,3,1,1,1,1] => 101001001111 => 010010011111
[2,4,1,2,1,1,1] => 101000110111 => 010001101111
[2,4,2,1,1,1,1] => 101000101111 => 010001011111
[2,5,1,1,1,1,1] => 101000011111 => 010000111111
[3,1,2,3,1,1,1] => 100110100111 => 001101001111
[3,1,3,1,2,1,1] => 100110011011 => 001100110111
[3,1,4,1,1,1,1] => 100110001111 => 001100011111
[3,2,1,2,2,1,1] => 100101101011 => 001011010111
[3,2,1,3,1,1,1] => 100101100111 => 001011001111
[4,1,1,2,2,1,1] => 100011101011 => 000111010111
[4,1,1,3,1,1,1] => 100011100111 => 000111001111
[3,3,1,1,2,1,1] => 100100111011 => 001001110111
[4,1,2,1,2,1,1] => 100011011011 => 000110110111
[4,2,1,1,2,1,1] => 100010111011 => 000101110111
[5,1,1,1,2,1,1] => 100001111011 => 000011110111
[3,2,2,2,1,1,1] => 100101010111 => 001010101111
[3,2,3,1,1,1,1] => 100101001111 => 001010011111
[3,3,2,1,1,1,1] => 100100101111 => 001001011111
[3,4,1,1,1,1,1] => 100100011111 => 001000111111
[4,1,2,2,1,1,1] => 100011010111 => 000110101111
[4,1,3,1,1,1,1] => 100011001111 => 000110011111
[4,2,1,2,1,1,1] => 100010110111 => 000101101111
[4,2,2,1,1,1,1] => 100010101111 => 000101011111
[4,3,1,1,1,1,1] => 100010011111 => 000100111111
[5,1,2,1,1,1,1] => 100001101111 => 000011011111
[5,2,1,1,1,1,1] => 100001011111 => 000010111111
[6,1,1,1,1,1,1] => 100000111111 => 000001111111
[11] => 10000000000 => 00000000001
[1,1,2,3,2,3] => 111010010100 => 110100101001
[1,2,2,2,2,3] => 110101010100 => 101010101001
[2,3,2,5] => 101001010000 => 010010100001
[5,1,1,1,1,2] => 10000111110 => 00001111101
[1,1,1,1,1,1,1,1,2,1] => 11111111101 => 11111111011
[1,1,1,1,1,1,1,1,1,1,1] => 11111111111 => 11111111111
[1,1,1,1,1,1,1,3,1] => 11111111001 => 11111110011
[1,1,1,1,1,5,1] => 11111100001 => 11111000011
[1,1,1,7,1] => 11110000001 => 11100000011
[1,1,1,2,1,2,1,1,1] => 11110110111 => 11101101111
[1,1,1,2,1,1,1,2,1] => 11110111101 => 11101111011
[1,3,1,1,1,1,1,1,1] => 11001111111 => 10011111111
[1,2,1,1,1,2,1,1,1] => 11011110111 => 10111101111
[1,2,2,1,2,2,1] => 11010110101 => 10101101011
[1,6,4] => 11000001000 => 10000010001
[1,4,6] => 11000100000 => 10001000001
[1,2,1,2,1,1,1,1,1,1] => 110110111111 => 101101111111
[1,2,1,1,1,1,1,2,1,1] => 110111111011 => 101111110111
[1,1,2,1,1,1,1,1,2,1] => 111011111101 => 110111111011
[1,1,1,1,1,2,1,2,1,1] => 111111011011 => 111110110111
[1,1,1,1,1,1,2,1,2,1] => 111111101101 => 111111011011
[1,2,2,2,4,1] => 110101010001 => 101010100011
[1,1,2,1,1,1,2,1,1] => 11101111011 => 11011110111
[1,1,2,2,2,1,1,1] => 11101010111 => 11010101111
[1,1,2,2,1,2,1,1] => 11101011011 => 11010110111
[1,1,2,1,2,2,1,1] => 11101101011 => 11011010111
[1,2,2,2,2,1,1] => 11010101011 => 10101010111
[1,1,2,2,2,4] => 111010101000 => 110101010001
Map
to binary word
Description
Return the composition as a binary word, treating ones as separators.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
Map
rotate front-to-back
Description
The rotation of a binary word, first letter last.
This is the word obtained by moving the first letter to the end.