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