Identifier
Values
0 => 1 => [1,1] => 11 => 0
1 => 0 => [2] => 10 => 1
00 => 11 => [1,1,1] => 111 => 0
01 => 10 => [1,2] => 110 => 1
10 => 01 => [2,1] => 101 => 2
11 => 00 => [3] => 100 => 3
000 => 111 => [1,1,1,1] => 1111 => 0
001 => 110 => [1,1,2] => 1110 => 1
010 => 101 => [1,2,1] => 1101 => 2
011 => 100 => [1,3] => 1100 => 3
100 => 011 => [2,1,1] => 1011 => 3
101 => 010 => [2,2] => 1010 => 3
110 => 001 => [3,1] => 1001 => 4
111 => 000 => [4] => 1000 => 5
0000 => 1111 => [1,1,1,1,1] => 11111 => 0
0001 => 1110 => [1,1,1,2] => 11110 => 1
0010 => 1101 => [1,1,2,1] => 11101 => 2
0011 => 1100 => [1,1,3] => 11100 => 3
0100 => 1011 => [1,2,1,1] => 11011 => 3
0101 => 1010 => [1,2,2] => 11010 => 3
0110 => 1001 => [1,3,1] => 11001 => 4
0111 => 1000 => [1,4] => 11000 => 5
1000 => 0111 => [2,1,1,1] => 10111 => 4
1001 => 0110 => [2,1,2] => 10110 => 4
1010 => 0101 => [2,2,1] => 10101 => 4
1011 => 0100 => [2,3] => 10100 => 5
1100 => 0011 => [3,1,1] => 10011 => 5
1101 => 0010 => [3,2] => 10010 => 5
1110 => 0001 => [4,1] => 10001 => 6
1111 => 0000 => [5] => 10000 => 7
00000 => 11111 => [1,1,1,1,1,1] => 111111 => 0
00001 => 11110 => [1,1,1,1,2] => 111110 => 1
00010 => 11101 => [1,1,1,2,1] => 111101 => 2
00011 => 11100 => [1,1,1,3] => 111100 => 3
00100 => 11011 => [1,1,2,1,1] => 111011 => 3
00101 => 11010 => [1,1,2,2] => 111010 => 3
00110 => 11001 => [1,1,3,1] => 111001 => 4
00111 => 11000 => [1,1,4] => 111000 => 5
01000 => 10111 => [1,2,1,1,1] => 110111 => 4
01001 => 10110 => [1,2,1,2] => 110110 => 4
01010 => 10101 => [1,2,2,1] => 110101 => 4
01011 => 10100 => [1,2,3] => 110100 => 5
01100 => 10011 => [1,3,1,1] => 110011 => 5
01101 => 10010 => [1,3,2] => 110010 => 5
01110 => 10001 => [1,4,1] => 110001 => 6
01111 => 10000 => [1,5] => 110000 => 7
10000 => 01111 => [2,1,1,1,1] => 101111 => 5
10001 => 01110 => [2,1,1,2] => 101110 => 5
10010 => 01101 => [2,1,2,1] => 101101 => 5
10011 => 01100 => [2,1,3] => 101100 => 5
10100 => 01011 => [2,2,1,1] => 101011 => 5
10101 => 01010 => [2,2,2] => 101010 => 5
10110 => 01001 => [2,3,1] => 101001 => 6
10111 => 01000 => [2,4] => 101000 => 7
11000 => 00111 => [3,1,1,1] => 100111 => 6
11001 => 00110 => [3,1,2] => 100110 => 6
11010 => 00101 => [3,2,1] => 100101 => 6
11011 => 00100 => [3,3] => 100100 => 7
11100 => 00011 => [4,1,1] => 100011 => 7
11101 => 00010 => [4,2] => 100010 => 7
11110 => 00001 => [5,1] => 100001 => 8
11111 => 00000 => [6] => 100000 => 9
000000 => 111111 => [1,1,1,1,1,1,1] => 1111111 => 0
000001 => 111110 => [1,1,1,1,1,2] => 1111110 => 1
000010 => 111101 => [1,1,1,1,2,1] => 1111101 => 2
000011 => 111100 => [1,1,1,1,3] => 1111100 => 3
000100 => 111011 => [1,1,1,2,1,1] => 1111011 => 3
000101 => 111010 => [1,1,1,2,2] => 1111010 => 3
000110 => 111001 => [1,1,1,3,1] => 1111001 => 4
000111 => 111000 => [1,1,1,4] => 1111000 => 5
001000 => 110111 => [1,1,2,1,1,1] => 1110111 => 4
001001 => 110110 => [1,1,2,1,2] => 1110110 => 4
001010 => 110101 => [1,1,2,2,1] => 1110101 => 4
001011 => 110100 => [1,1,2,3] => 1110100 => 5
001100 => 110011 => [1,1,3,1,1] => 1110011 => 5
001101 => 110010 => [1,1,3,2] => 1110010 => 5
001110 => 110001 => [1,1,4,1] => 1110001 => 6
001111 => 110000 => [1,1,5] => 1110000 => 7
010000 => 101111 => [1,2,1,1,1,1] => 1101111 => 5
010001 => 101110 => [1,2,1,1,2] => 1101110 => 5
010010 => 101101 => [1,2,1,2,1] => 1101101 => 5
010011 => 101100 => [1,2,1,3] => 1101100 => 5
010100 => 101011 => [1,2,2,1,1] => 1101011 => 5
010101 => 101010 => [1,2,2,2] => 1101010 => 5
010110 => 101001 => [1,2,3,1] => 1101001 => 6
010111 => 101000 => [1,2,4] => 1101000 => 7
011000 => 100111 => [1,3,1,1,1] => 1100111 => 6
011001 => 100110 => [1,3,1,2] => 1100110 => 6
011010 => 100101 => [1,3,2,1] => 1100101 => 6
011011 => 100100 => [1,3,3] => 1100100 => 7
011100 => 100011 => [1,4,1,1] => 1100011 => 7
011101 => 100010 => [1,4,2] => 1100010 => 7
011110 => 100001 => [1,5,1] => 1100001 => 8
011111 => 100000 => [1,6] => 1100000 => 9
100000 => 011111 => [2,1,1,1,1,1] => 1011111 => 6
100001 => 011110 => [2,1,1,1,2] => 1011110 => 6
100010 => 011101 => [2,1,1,2,1] => 1011101 => 6
100011 => 011100 => [2,1,1,3] => 1011100 => 6
100100 => 011011 => [2,1,2,1,1] => 1011011 => 6
100101 => 011010 => [2,1,2,2] => 1011010 => 6
100110 => 011001 => [2,1,3,1] => 1011001 => 6
>>> Load all 511 entries. <<<
100111 => 011000 => [2,1,4] => 1011000 => 7
101000 => 010111 => [2,2,1,1,1] => 1010111 => 6
101001 => 010110 => [2,2,1,2] => 1010110 => 6
101010 => 010101 => [2,2,2,1] => 1010101 => 6
101011 => 010100 => [2,2,3] => 1010100 => 7
101100 => 010011 => [2,3,1,1] => 1010011 => 7
101101 => 010010 => [2,3,2] => 1010010 => 7
101110 => 010001 => [2,4,1] => 1010001 => 8
101111 => 010000 => [2,5] => 1010000 => 9
110000 => 001111 => [3,1,1,1,1] => 1001111 => 7
110001 => 001110 => [3,1,1,2] => 1001110 => 7
110010 => 001101 => [3,1,2,1] => 1001101 => 7
110011 => 001100 => [3,1,3] => 1001100 => 7
110100 => 001011 => [3,2,1,1] => 1001011 => 7
110101 => 001010 => [3,2,2] => 1001010 => 7
110110 => 001001 => [3,3,1] => 1001001 => 8
110111 => 001000 => [3,4] => 1001000 => 9
111000 => 000111 => [4,1,1,1] => 1000111 => 8
111001 => 000110 => [4,1,2] => 1000110 => 8
111010 => 000101 => [4,2,1] => 1000101 => 8
111011 => 000100 => [4,3] => 1000100 => 9
111100 => 000011 => [5,1,1] => 1000011 => 9
111101 => 000010 => [5,2] => 1000010 => 9
111110 => 000001 => [6,1] => 1000001 => 10
111111 => 000000 => [7] => 1000000 => 11
0000000 => 1111111 => [1,1,1,1,1,1,1,1] => 11111111 => 0
0000001 => 1111110 => [1,1,1,1,1,1,2] => 11111110 => 1
0000010 => 1111101 => [1,1,1,1,1,2,1] => 11111101 => 2
0000011 => 1111100 => [1,1,1,1,1,3] => 11111100 => 3
0000100 => 1111011 => [1,1,1,1,2,1,1] => 11111011 => 3
0000101 => 1111010 => [1,1,1,1,2,2] => 11111010 => 3
0000110 => 1111001 => [1,1,1,1,3,1] => 11111001 => 4
0000111 => 1111000 => [1,1,1,1,4] => 11111000 => 5
0001000 => 1110111 => [1,1,1,2,1,1,1] => 11110111 => 4
0001001 => 1110110 => [1,1,1,2,1,2] => 11110110 => 4
0001010 => 1110101 => [1,1,1,2,2,1] => 11110101 => 4
0001011 => 1110100 => [1,1,1,2,3] => 11110100 => 5
0001100 => 1110011 => [1,1,1,3,1,1] => 11110011 => 5
0001101 => 1110010 => [1,1,1,3,2] => 11110010 => 5
0001110 => 1110001 => [1,1,1,4,1] => 11110001 => 6
0001111 => 1110000 => [1,1,1,5] => 11110000 => 7
0010000 => 1101111 => [1,1,2,1,1,1,1] => 11101111 => 5
0010001 => 1101110 => [1,1,2,1,1,2] => 11101110 => 5
0010010 => 1101101 => [1,1,2,1,2,1] => 11101101 => 5
0010011 => 1101100 => [1,1,2,1,3] => 11101100 => 5
0010100 => 1101011 => [1,1,2,2,1,1] => 11101011 => 5
0010101 => 1101010 => [1,1,2,2,2] => 11101010 => 5
0010110 => 1101001 => [1,1,2,3,1] => 11101001 => 6
0010111 => 1101000 => [1,1,2,4] => 11101000 => 7
0011000 => 1100111 => [1,1,3,1,1,1] => 11100111 => 6
0011001 => 1100110 => [1,1,3,1,2] => 11100110 => 6
0011010 => 1100101 => [1,1,3,2,1] => 11100101 => 6
0011011 => 1100100 => [1,1,3,3] => 11100100 => 7
0011100 => 1100011 => [1,1,4,1,1] => 11100011 => 7
0011101 => 1100010 => [1,1,4,2] => 11100010 => 7
0011110 => 1100001 => [1,1,5,1] => 11100001 => 8
0011111 => 1100000 => [1,1,6] => 11100000 => 9
0100000 => 1011111 => [1,2,1,1,1,1,1] => 11011111 => 6
0100001 => 1011110 => [1,2,1,1,1,2] => 11011110 => 6
0100010 => 1011101 => [1,2,1,1,2,1] => 11011101 => 6
0100011 => 1011100 => [1,2,1,1,3] => 11011100 => 6
0100100 => 1011011 => [1,2,1,2,1,1] => 11011011 => 6
0100101 => 1011010 => [1,2,1,2,2] => 11011010 => 6
0100110 => 1011001 => [1,2,1,3,1] => 11011001 => 6
0100111 => 1011000 => [1,2,1,4] => 11011000 => 7
0101000 => 1010111 => [1,2,2,1,1,1] => 11010111 => 6
0101001 => 1010110 => [1,2,2,1,2] => 11010110 => 6
0101010 => 1010101 => [1,2,2,2,1] => 11010101 => 6
0101011 => 1010100 => [1,2,2,3] => 11010100 => 7
0101100 => 1010011 => [1,2,3,1,1] => 11010011 => 7
0101101 => 1010010 => [1,2,3,2] => 11010010 => 7
0101110 => 1010001 => [1,2,4,1] => 11010001 => 8
0101111 => 1010000 => [1,2,5] => 11010000 => 9
0110000 => 1001111 => [1,3,1,1,1,1] => 11001111 => 7
0110001 => 1001110 => [1,3,1,1,2] => 11001110 => 7
0110010 => 1001101 => [1,3,1,2,1] => 11001101 => 7
0110011 => 1001100 => [1,3,1,3] => 11001100 => 7
0110100 => 1001011 => [1,3,2,1,1] => 11001011 => 7
0110101 => 1001010 => [1,3,2,2] => 11001010 => 7
0110110 => 1001001 => [1,3,3,1] => 11001001 => 8
0110111 => 1001000 => [1,3,4] => 11001000 => 9
0111000 => 1000111 => [1,4,1,1,1] => 11000111 => 8
0111001 => 1000110 => [1,4,1,2] => 11000110 => 8
0111010 => 1000101 => [1,4,2,1] => 11000101 => 8
0111011 => 1000100 => [1,4,3] => 11000100 => 9
0111100 => 1000011 => [1,5,1,1] => 11000011 => 9
0111101 => 1000010 => [1,5,2] => 11000010 => 9
0111110 => 1000001 => [1,6,1] => 11000001 => 10
0111111 => 1000000 => [1,7] => 11000000 => 11
1000000 => 0111111 => [2,1,1,1,1,1,1] => 10111111 => 7
1000001 => 0111110 => [2,1,1,1,1,2] => 10111110 => 7
1000010 => 0111101 => [2,1,1,1,2,1] => 10111101 => 7
1000011 => 0111100 => [2,1,1,1,3] => 10111100 => 7
1000100 => 0111011 => [2,1,1,2,1,1] => 10111011 => 7
1000101 => 0111010 => [2,1,1,2,2] => 10111010 => 7
1000110 => 0111001 => [2,1,1,3,1] => 10111001 => 7
1000111 => 0111000 => [2,1,1,4] => 10111000 => 7
1001000 => 0110111 => [2,1,2,1,1,1] => 10110111 => 7
1001001 => 0110110 => [2,1,2,1,2] => 10110110 => 7
1001010 => 0110101 => [2,1,2,2,1] => 10110101 => 7
1001011 => 0110100 => [2,1,2,3] => 10110100 => 7
1001100 => 0110011 => [2,1,3,1,1] => 10110011 => 7
1001101 => 0110010 => [2,1,3,2] => 10110010 => 7
1001110 => 0110001 => [2,1,4,1] => 10110001 => 8
1001111 => 0110000 => [2,1,5] => 10110000 => 9
1010000 => 0101111 => [2,2,1,1,1,1] => 10101111 => 7
1010001 => 0101110 => [2,2,1,1,2] => 10101110 => 7
1010010 => 0101101 => [2,2,1,2,1] => 10101101 => 7
1010011 => 0101100 => [2,2,1,3] => 10101100 => 7
1010100 => 0101011 => [2,2,2,1,1] => 10101011 => 7
1010101 => 0101010 => [2,2,2,2] => 10101010 => 7
1010110 => 0101001 => [2,2,3,1] => 10101001 => 8
1010111 => 0101000 => [2,2,4] => 10101000 => 9
1011000 => 0100111 => [2,3,1,1,1] => 10100111 => 8
1011001 => 0100110 => [2,3,1,2] => 10100110 => 8
1011010 => 0100101 => [2,3,2,1] => 10100101 => 8
1011011 => 0100100 => [2,3,3] => 10100100 => 9
1011100 => 0100011 => [2,4,1,1] => 10100011 => 9
1011101 => 0100010 => [2,4,2] => 10100010 => 9
1011110 => 0100001 => [2,5,1] => 10100001 => 10
1011111 => 0100000 => [2,6] => 10100000 => 11
1100000 => 0011111 => [3,1,1,1,1,1] => 10011111 => 8
1100001 => 0011110 => [3,1,1,1,2] => 10011110 => 8
1100010 => 0011101 => [3,1,1,2,1] => 10011101 => 8
1100011 => 0011100 => [3,1,1,3] => 10011100 => 8
1100100 => 0011011 => [3,1,2,1,1] => 10011011 => 8
1100101 => 0011010 => [3,1,2,2] => 10011010 => 8
1100110 => 0011001 => [3,1,3,1] => 10011001 => 8
1100111 => 0011000 => [3,1,4] => 10011000 => 9
1101000 => 0010111 => [3,2,1,1,1] => 10010111 => 8
1101001 => 0010110 => [3,2,1,2] => 10010110 => 8
1101010 => 0010101 => [3,2,2,1] => 10010101 => 8
1101011 => 0010100 => [3,2,3] => 10010100 => 9
1101100 => 0010011 => [3,3,1,1] => 10010011 => 9
1101101 => 0010010 => [3,3,2] => 10010010 => 9
1101110 => 0010001 => [3,4,1] => 10010001 => 10
1101111 => 0010000 => [3,5] => 10010000 => 11
1110000 => 0001111 => [4,1,1,1,1] => 10001111 => 9
1110001 => 0001110 => [4,1,1,2] => 10001110 => 9
1110010 => 0001101 => [4,1,2,1] => 10001101 => 9
1110011 => 0001100 => [4,1,3] => 10001100 => 9
1110100 => 0001011 => [4,2,1,1] => 10001011 => 9
1110101 => 0001010 => [4,2,2] => 10001010 => 9
1110110 => 0001001 => [4,3,1] => 10001001 => 10
1110111 => 0001000 => [4,4] => 10001000 => 11
1111000 => 0000111 => [5,1,1,1] => 10000111 => 10
1111001 => 0000110 => [5,1,2] => 10000110 => 10
1111010 => 0000101 => [5,2,1] => 10000101 => 10
1111011 => 0000100 => [5,3] => 10000100 => 11
1111100 => 0000011 => [6,1,1] => 10000011 => 11
1111101 => 0000010 => [6,2] => 10000010 => 11
1111110 => 0000001 => [7,1] => 10000001 => 12
1111111 => 0000000 => [8] => 10000000 => 13
00000000 => 11111111 => [1,1,1,1,1,1,1,1,1] => 111111111 => 0
00000001 => 11111110 => [1,1,1,1,1,1,1,2] => 111111110 => 1
00000010 => 11111101 => [1,1,1,1,1,1,2,1] => 111111101 => 2
00000011 => 11111100 => [1,1,1,1,1,1,3] => 111111100 => 3
00000100 => 11111011 => [1,1,1,1,1,2,1,1] => 111111011 => 3
00000101 => 11111010 => [1,1,1,1,1,2,2] => 111111010 => 3
00000110 => 11111001 => [1,1,1,1,1,3,1] => 111111001 => 4
00000111 => 11111000 => [1,1,1,1,1,4] => 111111000 => 5
00001000 => 11110111 => [1,1,1,1,2,1,1,1] => 111110111 => 4
00001001 => 11110110 => [1,1,1,1,2,1,2] => 111110110 => 4
00001010 => 11110101 => [1,1,1,1,2,2,1] => 111110101 => 4
00001011 => 11110100 => [1,1,1,1,2,3] => 111110100 => 5
00001100 => 11110011 => [1,1,1,1,3,1,1] => 111110011 => 5
00001101 => 11110010 => [1,1,1,1,3,2] => 111110010 => 5
00001110 => 11110001 => [1,1,1,1,4,1] => 111110001 => 6
00001111 => 11110000 => [1,1,1,1,5] => 111110000 => 7
00010000 => 11101111 => [1,1,1,2,1,1,1,1] => 111101111 => 5
00010001 => 11101110 => [1,1,1,2,1,1,2] => 111101110 => 5
00010010 => 11101101 => [1,1,1,2,1,2,1] => 111101101 => 5
00010011 => 11101100 => [1,1,1,2,1,3] => 111101100 => 5
00010100 => 11101011 => [1,1,1,2,2,1,1] => 111101011 => 5
00010101 => 11101010 => [1,1,1,2,2,2] => 111101010 => 5
00010110 => 11101001 => [1,1,1,2,3,1] => 111101001 => 6
00010111 => 11101000 => [1,1,1,2,4] => 111101000 => 7
00011000 => 11100111 => [1,1,1,3,1,1,1] => 111100111 => 6
00011001 => 11100110 => [1,1,1,3,1,2] => 111100110 => 6
00011010 => 11100101 => [1,1,1,3,2,1] => 111100101 => 6
00011011 => 11100100 => [1,1,1,3,3] => 111100100 => 7
00011100 => 11100011 => [1,1,1,4,1,1] => 111100011 => 7
00011101 => 11100010 => [1,1,1,4,2] => 111100010 => 7
00011110 => 11100001 => [1,1,1,5,1] => 111100001 => 8
00011111 => 11100000 => [1,1,1,6] => 111100000 => 9
00100000 => 11011111 => [1,1,2,1,1,1,1,1] => 111011111 => 6
00100001 => 11011110 => [1,1,2,1,1,1,2] => 111011110 => 6
00100010 => 11011101 => [1,1,2,1,1,2,1] => 111011101 => 6
00100011 => 11011100 => [1,1,2,1,1,3] => 111011100 => 6
00100100 => 11011011 => [1,1,2,1,2,1,1] => 111011011 => 6
00100101 => 11011010 => [1,1,2,1,2,2] => 111011010 => 6
00100110 => 11011001 => [1,1,2,1,3,1] => 111011001 => 6
00100111 => 11011000 => [1,1,2,1,4] => 111011000 => 7
00101000 => 11010111 => [1,1,2,2,1,1,1] => 111010111 => 6
00101001 => 11010110 => [1,1,2,2,1,2] => 111010110 => 6
00101010 => 11010101 => [1,1,2,2,2,1] => 111010101 => 6
00101011 => 11010100 => [1,1,2,2,3] => 111010100 => 7
00101100 => 11010011 => [1,1,2,3,1,1] => 111010011 => 7
00101101 => 11010010 => [1,1,2,3,2] => 111010010 => 7
00101110 => 11010001 => [1,1,2,4,1] => 111010001 => 8
00101111 => 11010000 => [1,1,2,5] => 111010000 => 9
00110000 => 11001111 => [1,1,3,1,1,1,1] => 111001111 => 7
00110001 => 11001110 => [1,1,3,1,1,2] => 111001110 => 7
00110010 => 11001101 => [1,1,3,1,2,1] => 111001101 => 7
00110011 => 11001100 => [1,1,3,1,3] => 111001100 => 7
00110100 => 11001011 => [1,1,3,2,1,1] => 111001011 => 7
00110101 => 11001010 => [1,1,3,2,2] => 111001010 => 7
00110110 => 11001001 => [1,1,3,3,1] => 111001001 => 8
00110111 => 11001000 => [1,1,3,4] => 111001000 => 9
00111000 => 11000111 => [1,1,4,1,1,1] => 111000111 => 8
00111001 => 11000110 => [1,1,4,1,2] => 111000110 => 8
00111010 => 11000101 => [1,1,4,2,1] => 111000101 => 8
00111011 => 11000100 => [1,1,4,3] => 111000100 => 9
00111100 => 11000011 => [1,1,5,1,1] => 111000011 => 9
00111101 => 11000010 => [1,1,5,2] => 111000010 => 9
00111110 => 11000001 => [1,1,6,1] => 111000001 => 10
00111111 => 11000000 => [1,1,7] => 111000000 => 11
01000000 => 10111111 => [1,2,1,1,1,1,1,1] => 110111111 => 7
01000001 => 10111110 => [1,2,1,1,1,1,2] => 110111110 => 7
01000010 => 10111101 => [1,2,1,1,1,2,1] => 110111101 => 7
01000011 => 10111100 => [1,2,1,1,1,3] => 110111100 => 7
01000100 => 10111011 => [1,2,1,1,2,1,1] => 110111011 => 7
01000101 => 10111010 => [1,2,1,1,2,2] => 110111010 => 7
01000110 => 10111001 => [1,2,1,1,3,1] => 110111001 => 7
01000111 => 10111000 => [1,2,1,1,4] => 110111000 => 7
01001000 => 10110111 => [1,2,1,2,1,1,1] => 110110111 => 7
01001001 => 10110110 => [1,2,1,2,1,2] => 110110110 => 7
01001010 => 10110101 => [1,2,1,2,2,1] => 110110101 => 7
01001011 => 10110100 => [1,2,1,2,3] => 110110100 => 7
01001100 => 10110011 => [1,2,1,3,1,1] => 110110011 => 7
01001101 => 10110010 => [1,2,1,3,2] => 110110010 => 7
01001110 => 10110001 => [1,2,1,4,1] => 110110001 => 8
01001111 => 10110000 => [1,2,1,5] => 110110000 => 9
01010000 => 10101111 => [1,2,2,1,1,1,1] => 110101111 => 7
01010001 => 10101110 => [1,2,2,1,1,2] => 110101110 => 7
01010010 => 10101101 => [1,2,2,1,2,1] => 110101101 => 7
01010011 => 10101100 => [1,2,2,1,3] => 110101100 => 7
01010100 => 10101011 => [1,2,2,2,1,1] => 110101011 => 7
01010101 => 10101010 => [1,2,2,2,2] => 110101010 => 7
01010110 => 10101001 => [1,2,2,3,1] => 110101001 => 8
01010111 => 10101000 => [1,2,2,4] => 110101000 => 9
01011000 => 10100111 => [1,2,3,1,1,1] => 110100111 => 8
01011001 => 10100110 => [1,2,3,1,2] => 110100110 => 8
01011010 => 10100101 => [1,2,3,2,1] => 110100101 => 8
01011011 => 10100100 => [1,2,3,3] => 110100100 => 9
01011100 => 10100011 => [1,2,4,1,1] => 110100011 => 9
01011101 => 10100010 => [1,2,4,2] => 110100010 => 9
01011110 => 10100001 => [1,2,5,1] => 110100001 => 10
01011111 => 10100000 => [1,2,6] => 110100000 => 11
01100000 => 10011111 => [1,3,1,1,1,1,1] => 110011111 => 8
01100001 => 10011110 => [1,3,1,1,1,2] => 110011110 => 8
01100010 => 10011101 => [1,3,1,1,2,1] => 110011101 => 8
01100011 => 10011100 => [1,3,1,1,3] => 110011100 => 8
01100100 => 10011011 => [1,3,1,2,1,1] => 110011011 => 8
01100101 => 10011010 => [1,3,1,2,2] => 110011010 => 8
01100110 => 10011001 => [1,3,1,3,1] => 110011001 => 8
01100111 => 10011000 => [1,3,1,4] => 110011000 => 9
01101000 => 10010111 => [1,3,2,1,1,1] => 110010111 => 8
01101001 => 10010110 => [1,3,2,1,2] => 110010110 => 8
01101010 => 10010101 => [1,3,2,2,1] => 110010101 => 8
01101011 => 10010100 => [1,3,2,3] => 110010100 => 9
01101100 => 10010011 => [1,3,3,1,1] => 110010011 => 9
01101101 => 10010010 => [1,3,3,2] => 110010010 => 9
01101110 => 10010001 => [1,3,4,1] => 110010001 => 10
01101111 => 10010000 => [1,3,5] => 110010000 => 11
01110000 => 10001111 => [1,4,1,1,1,1] => 110001111 => 9
01110001 => 10001110 => [1,4,1,1,2] => 110001110 => 9
01110010 => 10001101 => [1,4,1,2,1] => 110001101 => 9
01110011 => 10001100 => [1,4,1,3] => 110001100 => 9
01110100 => 10001011 => [1,4,2,1,1] => 110001011 => 9
01110101 => 10001010 => [1,4,2,2] => 110001010 => 9
01110110 => 10001001 => [1,4,3,1] => 110001001 => 10
01110111 => 10001000 => [1,4,4] => 110001000 => 11
01111000 => 10000111 => [1,5,1,1,1] => 110000111 => 10
01111001 => 10000110 => [1,5,1,2] => 110000110 => 10
01111010 => 10000101 => [1,5,2,1] => 110000101 => 10
01111011 => 10000100 => [1,5,3] => 110000100 => 11
01111100 => 10000011 => [1,6,1,1] => 110000011 => 11
01111101 => 10000010 => [1,6,2] => 110000010 => 11
01111110 => 10000001 => [1,7,1] => 110000001 => 12
01111111 => 10000000 => [1,8] => 110000000 => 13
10000000 => 01111111 => [2,1,1,1,1,1,1,1] => 101111111 => 8
10000001 => 01111110 => [2,1,1,1,1,1,2] => 101111110 => 8
10000010 => 01111101 => [2,1,1,1,1,2,1] => 101111101 => 8
10000011 => 01111100 => [2,1,1,1,1,3] => 101111100 => 8
10000100 => 01111011 => [2,1,1,1,2,1,1] => 101111011 => 8
10000101 => 01111010 => [2,1,1,1,2,2] => 101111010 => 8
10000110 => 01111001 => [2,1,1,1,3,1] => 101111001 => 8
10000111 => 01111000 => [2,1,1,1,4] => 101111000 => 8
10001000 => 01110111 => [2,1,1,2,1,1,1] => 101110111 => 8
10001001 => 01110110 => [2,1,1,2,1,2] => 101110110 => 8
10001010 => 01110101 => [2,1,1,2,2,1] => 101110101 => 8
10001011 => 01110100 => [2,1,1,2,3] => 101110100 => 8
10001100 => 01110011 => [2,1,1,3,1,1] => 101110011 => 8
10001101 => 01110010 => [2,1,1,3,2] => 101110010 => 8
10001110 => 01110001 => [2,1,1,4,1] => 101110001 => 8
10001111 => 01110000 => [2,1,1,5] => 101110000 => 9
10010000 => 01101111 => [2,1,2,1,1,1,1] => 101101111 => 8
10010001 => 01101110 => [2,1,2,1,1,2] => 101101110 => 8
10010010 => 01101101 => [2,1,2,1,2,1] => 101101101 => 8
10010011 => 01101100 => [2,1,2,1,3] => 101101100 => 8
10010100 => 01101011 => [2,1,2,2,1,1] => 101101011 => 8
10010101 => 01101010 => [2,1,2,2,2] => 101101010 => 8
10010110 => 01101001 => [2,1,2,3,1] => 101101001 => 8
10010111 => 01101000 => [2,1,2,4] => 101101000 => 9
10011000 => 01100111 => [2,1,3,1,1,1] => 101100111 => 8
10011001 => 01100110 => [2,1,3,1,2] => 101100110 => 8
10011010 => 01100101 => [2,1,3,2,1] => 101100101 => 8
10011011 => 01100100 => [2,1,3,3] => 101100100 => 9
10011100 => 01100011 => [2,1,4,1,1] => 101100011 => 9
10011101 => 01100010 => [2,1,4,2] => 101100010 => 9
10011110 => 01100001 => [2,1,5,1] => 101100001 => 10
10011111 => 01100000 => [2,1,6] => 101100000 => 11
10100000 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 8
10100001 => 01011110 => [2,2,1,1,1,2] => 101011110 => 8
10100010 => 01011101 => [2,2,1,1,2,1] => 101011101 => 8
10100011 => 01011100 => [2,2,1,1,3] => 101011100 => 8
10100100 => 01011011 => [2,2,1,2,1,1] => 101011011 => 8
10100101 => 01011010 => [2,2,1,2,2] => 101011010 => 8
10100110 => 01011001 => [2,2,1,3,1] => 101011001 => 8
10100111 => 01011000 => [2,2,1,4] => 101011000 => 9
10101000 => 01010111 => [2,2,2,1,1,1] => 101010111 => 8
10101001 => 01010110 => [2,2,2,1,2] => 101010110 => 8
10101010 => 01010101 => [2,2,2,2,1] => 101010101 => 8
10101011 => 01010100 => [2,2,2,3] => 101010100 => 9
10101100 => 01010011 => [2,2,3,1,1] => 101010011 => 9
10101101 => 01010010 => [2,2,3,2] => 101010010 => 9
10101110 => 01010001 => [2,2,4,1] => 101010001 => 10
10101111 => 01010000 => [2,2,5] => 101010000 => 11
10110000 => 01001111 => [2,3,1,1,1,1] => 101001111 => 9
10110001 => 01001110 => [2,3,1,1,2] => 101001110 => 9
10110010 => 01001101 => [2,3,1,2,1] => 101001101 => 9
10110011 => 01001100 => [2,3,1,3] => 101001100 => 9
10110100 => 01001011 => [2,3,2,1,1] => 101001011 => 9
10110101 => 01001010 => [2,3,2,2] => 101001010 => 9
10110110 => 01001001 => [2,3,3,1] => 101001001 => 10
10110111 => 01001000 => [2,3,4] => 101001000 => 11
10111000 => 01000111 => [2,4,1,1,1] => 101000111 => 10
10111001 => 01000110 => [2,4,1,2] => 101000110 => 10
10111010 => 01000101 => [2,4,2,1] => 101000101 => 10
10111011 => 01000100 => [2,4,3] => 101000100 => 11
10111100 => 01000011 => [2,5,1,1] => 101000011 => 11
10111101 => 01000010 => [2,5,2] => 101000010 => 11
10111110 => 01000001 => [2,6,1] => 101000001 => 12
10111111 => 01000000 => [2,7] => 101000000 => 13
11000000 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 9
11000001 => 00111110 => [3,1,1,1,1,2] => 100111110 => 9
11000010 => 00111101 => [3,1,1,1,2,1] => 100111101 => 9
11000011 => 00111100 => [3,1,1,1,3] => 100111100 => 9
11000100 => 00111011 => [3,1,1,2,1,1] => 100111011 => 9
11000101 => 00111010 => [3,1,1,2,2] => 100111010 => 9
11000110 => 00111001 => [3,1,1,3,1] => 100111001 => 9
11000111 => 00111000 => [3,1,1,4] => 100111000 => 9
11001000 => 00110111 => [3,1,2,1,1,1] => 100110111 => 9
11001001 => 00110110 => [3,1,2,1,2] => 100110110 => 9
11001010 => 00110101 => [3,1,2,2,1] => 100110101 => 9
11001011 => 00110100 => [3,1,2,3] => 100110100 => 9
11001100 => 00110011 => [3,1,3,1,1] => 100110011 => 9
11001101 => 00110010 => [3,1,3,2] => 100110010 => 9
11001110 => 00110001 => [3,1,4,1] => 100110001 => 10
11001111 => 00110000 => [3,1,5] => 100110000 => 11
11010000 => 00101111 => [3,2,1,1,1,1] => 100101111 => 9
11010001 => 00101110 => [3,2,1,1,2] => 100101110 => 9
11010010 => 00101101 => [3,2,1,2,1] => 100101101 => 9
11010011 => 00101100 => [3,2,1,3] => 100101100 => 9
11010100 => 00101011 => [3,2,2,1,1] => 100101011 => 9
11010101 => 00101010 => [3,2,2,2] => 100101010 => 9
11010110 => 00101001 => [3,2,3,1] => 100101001 => 10
11010111 => 00101000 => [3,2,4] => 100101000 => 11
11011000 => 00100111 => [3,3,1,1,1] => 100100111 => 10
11011001 => 00100110 => [3,3,1,2] => 100100110 => 10
11011010 => 00100101 => [3,3,2,1] => 100100101 => 10
11011011 => 00100100 => [3,3,3] => 100100100 => 11
11011100 => 00100011 => [3,4,1,1] => 100100011 => 11
11011101 => 00100010 => [3,4,2] => 100100010 => 11
11011110 => 00100001 => [3,5,1] => 100100001 => 12
11011111 => 00100000 => [3,6] => 100100000 => 13
11100000 => 00011111 => [4,1,1,1,1,1] => 100011111 => 10
11100001 => 00011110 => [4,1,1,1,2] => 100011110 => 10
11100010 => 00011101 => [4,1,1,2,1] => 100011101 => 10
11100011 => 00011100 => [4,1,1,3] => 100011100 => 10
11100100 => 00011011 => [4,1,2,1,1] => 100011011 => 10
11100101 => 00011010 => [4,1,2,2] => 100011010 => 10
11100110 => 00011001 => [4,1,3,1] => 100011001 => 10
11100111 => 00011000 => [4,1,4] => 100011000 => 11
11101000 => 00010111 => [4,2,1,1,1] => 100010111 => 10
11101001 => 00010110 => [4,2,1,2] => 100010110 => 10
11101010 => 00010101 => [4,2,2,1] => 100010101 => 10
11101011 => 00010100 => [4,2,3] => 100010100 => 11
11101100 => 00010011 => [4,3,1,1] => 100010011 => 11
11101101 => 00010010 => [4,3,2] => 100010010 => 11
11101110 => 00010001 => [4,4,1] => 100010001 => 12
11101111 => 00010000 => [4,5] => 100010000 => 13
11110000 => 00001111 => [5,1,1,1,1] => 100001111 => 11
11110001 => 00001110 => [5,1,1,2] => 100001110 => 11
11110010 => 00001101 => [5,1,2,1] => 100001101 => 11
11110011 => 00001100 => [5,1,3] => 100001100 => 11
11110100 => 00001011 => [5,2,1,1] => 100001011 => 11
11110101 => 00001010 => [5,2,2] => 100001010 => 11
11110110 => 00001001 => [5,3,1] => 100001001 => 12
11110111 => 00001000 => [5,4] => 100001000 => 13
11111000 => 00000111 => [6,1,1,1] => 100000111 => 12
11111001 => 00000110 => [6,1,2] => 100000110 => 12
11111010 => 00000101 => [6,2,1] => 100000101 => 12
11111011 => 00000100 => [6,3] => 100000100 => 13
11111100 => 00000011 => [7,1,1] => 100000011 => 13
11111101 => 00000010 => [7,2] => 100000010 => 13
11111110 => 00000001 => [8,1] => 100000001 => 14
11111111 => 00000000 => [9] => 100000000 => 15
=> => [1] => 1 => 0
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Description
The degree of a binary word.
A valley in a binary word is a letter $0$ which is not immediately followed by a $1$. A peak is a letter $1$ which is not immediately followed by a $0$.
Let $f$ be the map that replaces every valley with a peak. The degree of a binary word $w$ is the number of times $f$ has to be applied to obtain a binary word without zeros.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
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 $0$.