Identifier
Values
0 => 0 => [2] => 10 => 1
1 => 1 => [1,1] => 11 => 0
00 => 00 => [3] => 100 => 2
01 => 01 => [2,1] => 101 => 1
10 => 01 => [2,1] => 101 => 1
11 => 11 => [1,1,1] => 111 => 0
000 => 000 => [4] => 1000 => 3
001 => 001 => [3,1] => 1001 => 2
010 => 001 => [3,1] => 1001 => 2
011 => 011 => [2,1,1] => 1011 => 1
100 => 001 => [3,1] => 1001 => 2
101 => 011 => [2,1,1] => 1011 => 1
110 => 011 => [2,1,1] => 1011 => 1
111 => 111 => [1,1,1,1] => 1111 => 0
0000 => 0000 => [5] => 10000 => 4
0001 => 0001 => [4,1] => 10001 => 3
0010 => 0001 => [4,1] => 10001 => 3
0011 => 0011 => [3,1,1] => 10011 => 2
0100 => 0001 => [4,1] => 10001 => 3
0101 => 0101 => [2,2,1] => 10101 => 2
0110 => 0011 => [3,1,1] => 10011 => 2
0111 => 0111 => [2,1,1,1] => 10111 => 1
1000 => 0001 => [4,1] => 10001 => 3
1001 => 0011 => [3,1,1] => 10011 => 2
1010 => 0011 => [3,1,1] => 10011 => 2
1011 => 0111 => [2,1,1,1] => 10111 => 1
1100 => 0011 => [3,1,1] => 10011 => 2
1101 => 0111 => [2,1,1,1] => 10111 => 1
1110 => 0111 => [2,1,1,1] => 10111 => 1
1111 => 1111 => [1,1,1,1,1] => 11111 => 0
00000 => 00000 => [6] => 100000 => 5
00001 => 00001 => [5,1] => 100001 => 4
00010 => 00001 => [5,1] => 100001 => 4
00011 => 00011 => [4,1,1] => 100011 => 3
00100 => 00001 => [5,1] => 100001 => 4
00101 => 00101 => [3,2,1] => 100101 => 3
00110 => 00011 => [4,1,1] => 100011 => 3
00111 => 00111 => [3,1,1,1] => 100111 => 2
01000 => 00001 => [5,1] => 100001 => 4
01001 => 00101 => [3,2,1] => 100101 => 3
01010 => 00101 => [3,2,1] => 100101 => 3
01011 => 01011 => [2,2,1,1] => 101011 => 2
01100 => 00011 => [4,1,1] => 100011 => 3
01101 => 01011 => [2,2,1,1] => 101011 => 2
01110 => 00111 => [3,1,1,1] => 100111 => 2
01111 => 01111 => [2,1,1,1,1] => 101111 => 1
10000 => 00001 => [5,1] => 100001 => 4
10001 => 00011 => [4,1,1] => 100011 => 3
10010 => 00011 => [4,1,1] => 100011 => 3
10011 => 00111 => [3,1,1,1] => 100111 => 2
10100 => 00011 => [4,1,1] => 100011 => 3
10101 => 01011 => [2,2,1,1] => 101011 => 2
10110 => 00111 => [3,1,1,1] => 100111 => 2
10111 => 01111 => [2,1,1,1,1] => 101111 => 1
11000 => 00011 => [4,1,1] => 100011 => 3
11001 => 00111 => [3,1,1,1] => 100111 => 2
11010 => 00111 => [3,1,1,1] => 100111 => 2
11011 => 01111 => [2,1,1,1,1] => 101111 => 1
11100 => 00111 => [3,1,1,1] => 100111 => 2
11101 => 01111 => [2,1,1,1,1] => 101111 => 1
11110 => 01111 => [2,1,1,1,1] => 101111 => 1
11111 => 11111 => [1,1,1,1,1,1] => 111111 => 0
000000 => 000000 => [7] => 1000000 => 6
000001 => 000001 => [6,1] => 1000001 => 5
000010 => 000001 => [6,1] => 1000001 => 5
000011 => 000011 => [5,1,1] => 1000011 => 4
000100 => 000001 => [6,1] => 1000001 => 5
000101 => 000101 => [4,2,1] => 1000101 => 4
000110 => 000011 => [5,1,1] => 1000011 => 4
000111 => 000111 => [4,1,1,1] => 1000111 => 3
001000 => 000001 => [6,1] => 1000001 => 5
001001 => 001001 => [3,3,1] => 1001001 => 4
001010 => 000101 => [4,2,1] => 1000101 => 4
001011 => 001011 => [3,2,1,1] => 1001011 => 3
001100 => 000011 => [5,1,1] => 1000011 => 4
001101 => 001101 => [3,1,2,1] => 1001101 => 3
001110 => 000111 => [4,1,1,1] => 1000111 => 3
001111 => 001111 => [3,1,1,1,1] => 1001111 => 2
010000 => 000001 => [6,1] => 1000001 => 5
010001 => 000101 => [4,2,1] => 1000101 => 4
010010 => 000101 => [4,2,1] => 1000101 => 4
010011 => 001101 => [3,1,2,1] => 1001101 => 3
010100 => 000101 => [4,2,1] => 1000101 => 4
010101 => 010101 => [2,2,2,1] => 1010101 => 3
010110 => 001011 => [3,2,1,1] => 1001011 => 3
010111 => 010111 => [2,2,1,1,1] => 1010111 => 2
011000 => 000011 => [5,1,1] => 1000011 => 4
011001 => 001011 => [3,2,1,1] => 1001011 => 3
011010 => 001011 => [3,2,1,1] => 1001011 => 3
011011 => 011011 => [2,1,2,1,1] => 1011011 => 2
011100 => 000111 => [4,1,1,1] => 1000111 => 3
011101 => 010111 => [2,2,1,1,1] => 1010111 => 2
011110 => 001111 => [3,1,1,1,1] => 1001111 => 2
011111 => 011111 => [2,1,1,1,1,1] => 1011111 => 1
100000 => 000001 => [6,1] => 1000001 => 5
100001 => 000011 => [5,1,1] => 1000011 => 4
100010 => 000011 => [5,1,1] => 1000011 => 4
100011 => 000111 => [4,1,1,1] => 1000111 => 3
100100 => 000011 => [5,1,1] => 1000011 => 4
100101 => 001011 => [3,2,1,1] => 1001011 => 3
100110 => 000111 => [4,1,1,1] => 1000111 => 3
>>> Load all 511 entries. <<<
100111 => 001111 => [3,1,1,1,1] => 1001111 => 2
101000 => 000011 => [5,1,1] => 1000011 => 4
101001 => 001011 => [3,2,1,1] => 1001011 => 3
101010 => 001011 => [3,2,1,1] => 1001011 => 3
101011 => 010111 => [2,2,1,1,1] => 1010111 => 2
101100 => 000111 => [4,1,1,1] => 1000111 => 3
101101 => 010111 => [2,2,1,1,1] => 1010111 => 2
101110 => 001111 => [3,1,1,1,1] => 1001111 => 2
101111 => 011111 => [2,1,1,1,1,1] => 1011111 => 1
110000 => 000011 => [5,1,1] => 1000011 => 4
110001 => 000111 => [4,1,1,1] => 1000111 => 3
110010 => 000111 => [4,1,1,1] => 1000111 => 3
110011 => 001111 => [3,1,1,1,1] => 1001111 => 2
110100 => 000111 => [4,1,1,1] => 1000111 => 3
110101 => 010111 => [2,2,1,1,1] => 1010111 => 2
110110 => 001111 => [3,1,1,1,1] => 1001111 => 2
110111 => 011111 => [2,1,1,1,1,1] => 1011111 => 1
111000 => 000111 => [4,1,1,1] => 1000111 => 3
111001 => 001111 => [3,1,1,1,1] => 1001111 => 2
111010 => 001111 => [3,1,1,1,1] => 1001111 => 2
111011 => 011111 => [2,1,1,1,1,1] => 1011111 => 1
111100 => 001111 => [3,1,1,1,1] => 1001111 => 2
111101 => 011111 => [2,1,1,1,1,1] => 1011111 => 1
111110 => 011111 => [2,1,1,1,1,1] => 1011111 => 1
111111 => 111111 => [1,1,1,1,1,1,1] => 1111111 => 0
0000000 => 0000000 => [8] => 10000000 => 7
0000001 => 0000001 => [7,1] => 10000001 => 6
0000010 => 0000001 => [7,1] => 10000001 => 6
0000011 => 0000011 => [6,1,1] => 10000011 => 5
0000100 => 0000001 => [7,1] => 10000001 => 6
0000101 => 0000101 => [5,2,1] => 10000101 => 5
0000110 => 0000011 => [6,1,1] => 10000011 => 5
0000111 => 0000111 => [5,1,1,1] => 10000111 => 4
0001000 => 0000001 => [7,1] => 10000001 => 6
0001001 => 0001001 => [4,3,1] => 10001001 => 5
0001010 => 0000101 => [5,2,1] => 10000101 => 5
0001011 => 0001011 => [4,2,1,1] => 10001011 => 4
0001100 => 0000011 => [6,1,1] => 10000011 => 5
0001101 => 0001101 => [4,1,2,1] => 10001101 => 4
0001110 => 0000111 => [5,1,1,1] => 10000111 => 4
0001111 => 0001111 => [4,1,1,1,1] => 10001111 => 3
0010000 => 0000001 => [7,1] => 10000001 => 6
0010001 => 0001001 => [4,3,1] => 10001001 => 5
0010010 => 0001001 => [4,3,1] => 10001001 => 5
0010011 => 0010011 => [3,3,1,1] => 10010011 => 4
0010100 => 0000101 => [5,2,1] => 10000101 => 5
0010101 => 0010101 => [3,2,2,1] => 10010101 => 4
0010110 => 0001011 => [4,2,1,1] => 10001011 => 4
0010111 => 0010111 => [3,2,1,1,1] => 10010111 => 3
0011000 => 0000011 => [6,1,1] => 10000011 => 5
0011001 => 0010011 => [3,3,1,1] => 10010011 => 4
0011010 => 0001101 => [4,1,2,1] => 10001101 => 4
0011011 => 0011011 => [3,1,2,1,1] => 10011011 => 3
0011100 => 0000111 => [5,1,1,1] => 10000111 => 4
0011101 => 0011101 => [3,1,1,2,1] => 10011101 => 3
0011110 => 0001111 => [4,1,1,1,1] => 10001111 => 3
0011111 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
0100000 => 0000001 => [7,1] => 10000001 => 6
0100001 => 0000101 => [5,2,1] => 10000101 => 5
0100010 => 0000101 => [5,2,1] => 10000101 => 5
0100011 => 0001101 => [4,1,2,1] => 10001101 => 4
0100100 => 0000101 => [5,2,1] => 10000101 => 5
0100101 => 0010101 => [3,2,2,1] => 10010101 => 4
0100110 => 0001101 => [4,1,2,1] => 10001101 => 4
0100111 => 0011101 => [3,1,1,2,1] => 10011101 => 3
0101000 => 0000101 => [5,2,1] => 10000101 => 5
0101001 => 0010101 => [3,2,2,1] => 10010101 => 4
0101010 => 0010101 => [3,2,2,1] => 10010101 => 4
0101011 => 0101011 => [2,2,2,1,1] => 10101011 => 3
0101100 => 0001011 => [4,2,1,1] => 10001011 => 4
0101101 => 0101011 => [2,2,2,1,1] => 10101011 => 3
0101110 => 0010111 => [3,2,1,1,1] => 10010111 => 3
0101111 => 0101111 => [2,2,1,1,1,1] => 10101111 => 2
0110000 => 0000011 => [6,1,1] => 10000011 => 5
0110001 => 0001011 => [4,2,1,1] => 10001011 => 4
0110010 => 0001011 => [4,2,1,1] => 10001011 => 4
0110011 => 0011011 => [3,1,2,1,1] => 10011011 => 3
0110100 => 0001011 => [4,2,1,1] => 10001011 => 4
0110101 => 0101011 => [2,2,2,1,1] => 10101011 => 3
0110110 => 0011011 => [3,1,2,1,1] => 10011011 => 3
0110111 => 0110111 => [2,1,2,1,1,1] => 10110111 => 2
0111000 => 0000111 => [5,1,1,1] => 10000111 => 4
0111001 => 0010111 => [3,2,1,1,1] => 10010111 => 3
0111010 => 0010111 => [3,2,1,1,1] => 10010111 => 3
0111011 => 0110111 => [2,1,2,1,1,1] => 10110111 => 2
0111100 => 0001111 => [4,1,1,1,1] => 10001111 => 3
0111101 => 0101111 => [2,2,1,1,1,1] => 10101111 => 2
0111110 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
0111111 => 0111111 => [2,1,1,1,1,1,1] => 10111111 => 1
1000000 => 0000001 => [7,1] => 10000001 => 6
1000001 => 0000011 => [6,1,1] => 10000011 => 5
1000010 => 0000011 => [6,1,1] => 10000011 => 5
1000011 => 0000111 => [5,1,1,1] => 10000111 => 4
1000100 => 0000011 => [6,1,1] => 10000011 => 5
1000101 => 0001011 => [4,2,1,1] => 10001011 => 4
1000110 => 0000111 => [5,1,1,1] => 10000111 => 4
1000111 => 0001111 => [4,1,1,1,1] => 10001111 => 3
1001000 => 0000011 => [6,1,1] => 10000011 => 5
1001001 => 0010011 => [3,3,1,1] => 10010011 => 4
1001010 => 0001011 => [4,2,1,1] => 10001011 => 4
1001011 => 0010111 => [3,2,1,1,1] => 10010111 => 3
1001100 => 0000111 => [5,1,1,1] => 10000111 => 4
1001101 => 0011011 => [3,1,2,1,1] => 10011011 => 3
1001110 => 0001111 => [4,1,1,1,1] => 10001111 => 3
1001111 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
1010000 => 0000011 => [6,1,1] => 10000011 => 5
1010001 => 0001011 => [4,2,1,1] => 10001011 => 4
1010010 => 0001011 => [4,2,1,1] => 10001011 => 4
1010011 => 0011011 => [3,1,2,1,1] => 10011011 => 3
1010100 => 0001011 => [4,2,1,1] => 10001011 => 4
1010101 => 0101011 => [2,2,2,1,1] => 10101011 => 3
1010110 => 0010111 => [3,2,1,1,1] => 10010111 => 3
1010111 => 0101111 => [2,2,1,1,1,1] => 10101111 => 2
1011000 => 0000111 => [5,1,1,1] => 10000111 => 4
1011001 => 0010111 => [3,2,1,1,1] => 10010111 => 3
1011010 => 0010111 => [3,2,1,1,1] => 10010111 => 3
1011011 => 0110111 => [2,1,2,1,1,1] => 10110111 => 2
1011100 => 0001111 => [4,1,1,1,1] => 10001111 => 3
1011101 => 0101111 => [2,2,1,1,1,1] => 10101111 => 2
1011110 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
1011111 => 0111111 => [2,1,1,1,1,1,1] => 10111111 => 1
1100000 => 0000011 => [6,1,1] => 10000011 => 5
1100001 => 0000111 => [5,1,1,1] => 10000111 => 4
1100010 => 0000111 => [5,1,1,1] => 10000111 => 4
1100011 => 0001111 => [4,1,1,1,1] => 10001111 => 3
1100100 => 0000111 => [5,1,1,1] => 10000111 => 4
1100101 => 0010111 => [3,2,1,1,1] => 10010111 => 3
1100110 => 0001111 => [4,1,1,1,1] => 10001111 => 3
1100111 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
1101000 => 0000111 => [5,1,1,1] => 10000111 => 4
1101001 => 0010111 => [3,2,1,1,1] => 10010111 => 3
1101010 => 0010111 => [3,2,1,1,1] => 10010111 => 3
1101011 => 0101111 => [2,2,1,1,1,1] => 10101111 => 2
1101100 => 0001111 => [4,1,1,1,1] => 10001111 => 3
1101101 => 0101111 => [2,2,1,1,1,1] => 10101111 => 2
1101110 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
1101111 => 0111111 => [2,1,1,1,1,1,1] => 10111111 => 1
1110000 => 0000111 => [5,1,1,1] => 10000111 => 4
1110001 => 0001111 => [4,1,1,1,1] => 10001111 => 3
1110010 => 0001111 => [4,1,1,1,1] => 10001111 => 3
1110011 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
1110100 => 0001111 => [4,1,1,1,1] => 10001111 => 3
1110101 => 0101111 => [2,2,1,1,1,1] => 10101111 => 2
1110110 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
1110111 => 0111111 => [2,1,1,1,1,1,1] => 10111111 => 1
1111000 => 0001111 => [4,1,1,1,1] => 10001111 => 3
1111001 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
1111010 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
1111011 => 0111111 => [2,1,1,1,1,1,1] => 10111111 => 1
1111100 => 0011111 => [3,1,1,1,1,1] => 10011111 => 2
1111101 => 0111111 => [2,1,1,1,1,1,1] => 10111111 => 1
1111110 => 0111111 => [2,1,1,1,1,1,1] => 10111111 => 1
1111111 => 1111111 => [1,1,1,1,1,1,1,1] => 11111111 => 0
00000000 => 00000000 => [9] => 100000000 => 8
00000001 => 00000001 => [8,1] => 100000001 => 7
00000010 => 00000001 => [8,1] => 100000001 => 7
00000011 => 00000011 => [7,1,1] => 100000011 => 6
00000100 => 00000001 => [8,1] => 100000001 => 7
00000101 => 00000101 => [6,2,1] => 100000101 => 6
00000110 => 00000011 => [7,1,1] => 100000011 => 6
00000111 => 00000111 => [6,1,1,1] => 100000111 => 5
00001000 => 00000001 => [8,1] => 100000001 => 7
00001001 => 00001001 => [5,3,1] => 100001001 => 6
00001010 => 00000101 => [6,2,1] => 100000101 => 6
00001011 => 00001011 => [5,2,1,1] => 100001011 => 5
00001100 => 00000011 => [7,1,1] => 100000011 => 6
00001101 => 00001101 => [5,1,2,1] => 100001101 => 5
00001110 => 00000111 => [6,1,1,1] => 100000111 => 5
00001111 => 00001111 => [5,1,1,1,1] => 100001111 => 4
00010000 => 00000001 => [8,1] => 100000001 => 7
00010001 => 00010001 => [4,4,1] => 100010001 => 6
00010010 => 00001001 => [5,3,1] => 100001001 => 6
00010011 => 00010011 => [4,3,1,1] => 100010011 => 5
00010100 => 00000101 => [6,2,1] => 100000101 => 6
00010101 => 00010101 => [4,2,2,1] => 100010101 => 5
00010110 => 00001011 => [5,2,1,1] => 100001011 => 5
00010111 => 00010111 => [4,2,1,1,1] => 100010111 => 4
00011000 => 00000011 => [7,1,1] => 100000011 => 6
00011001 => 00011001 => [4,1,3,1] => 100011001 => 5
00011010 => 00001101 => [5,1,2,1] => 100001101 => 5
00011011 => 00011011 => [4,1,2,1,1] => 100011011 => 4
00011100 => 00000111 => [6,1,1,1] => 100000111 => 5
00011101 => 00011101 => [4,1,1,2,1] => 100011101 => 4
00011110 => 00001111 => [5,1,1,1,1] => 100001111 => 4
00011111 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
00100000 => 00000001 => [8,1] => 100000001 => 7
00100001 => 00001001 => [5,3,1] => 100001001 => 6
00100010 => 00001001 => [5,3,1] => 100001001 => 6
00100011 => 00011001 => [4,1,3,1] => 100011001 => 5
00100100 => 00001001 => [5,3,1] => 100001001 => 6
00100101 => 00100101 => [3,3,2,1] => 100100101 => 5
00100110 => 00010011 => [4,3,1,1] => 100010011 => 5
00100111 => 00100111 => [3,3,1,1,1] => 100100111 => 4
00101000 => 00000101 => [6,2,1] => 100000101 => 6
00101001 => 00100101 => [3,3,2,1] => 100100101 => 5
00101010 => 00010101 => [4,2,2,1] => 100010101 => 5
00101011 => 00101011 => [3,2,2,1,1] => 100101011 => 4
00101100 => 00001011 => [5,2,1,1] => 100001011 => 5
00101101 => 00101011 => [3,2,2,1,1] => 100101011 => 4
00101110 => 00010111 => [4,2,1,1,1] => 100010111 => 4
00101111 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
00110000 => 00000011 => [7,1,1] => 100000011 => 6
00110001 => 00010011 => [4,3,1,1] => 100010011 => 5
00110010 => 00010011 => [4,3,1,1] => 100010011 => 5
00110011 => 00110011 => [3,1,3,1,1] => 100110011 => 4
00110100 => 00001101 => [5,1,2,1] => 100001101 => 5
00110101 => 00110101 => [3,1,2,2,1] => 100110101 => 4
00110110 => 00011011 => [4,1,2,1,1] => 100011011 => 4
00110111 => 00110111 => [3,1,2,1,1,1] => 100110111 => 3
00111000 => 00000111 => [6,1,1,1] => 100000111 => 5
00111001 => 00100111 => [3,3,1,1,1] => 100100111 => 4
00111010 => 00011101 => [4,1,1,2,1] => 100011101 => 4
00111011 => 00111011 => [3,1,1,2,1,1] => 100111011 => 3
00111100 => 00001111 => [5,1,1,1,1] => 100001111 => 4
00111101 => 00111101 => [3,1,1,1,2,1] => 100111101 => 3
00111110 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
00111111 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
01000000 => 00000001 => [8,1] => 100000001 => 7
01000001 => 00000101 => [6,2,1] => 100000101 => 6
01000010 => 00000101 => [6,2,1] => 100000101 => 6
01000011 => 00001101 => [5,1,2,1] => 100001101 => 5
01000100 => 00000101 => [6,2,1] => 100000101 => 6
01000101 => 00010101 => [4,2,2,1] => 100010101 => 5
01000110 => 00001101 => [5,1,2,1] => 100001101 => 5
01000111 => 00011101 => [4,1,1,2,1] => 100011101 => 4
01001000 => 00000101 => [6,2,1] => 100000101 => 6
01001001 => 00100101 => [3,3,2,1] => 100100101 => 5
01001010 => 00010101 => [4,2,2,1] => 100010101 => 5
01001011 => 00101011 => [3,2,2,1,1] => 100101011 => 4
01001100 => 00001101 => [5,1,2,1] => 100001101 => 5
01001101 => 00110101 => [3,1,2,2,1] => 100110101 => 4
01001110 => 00011101 => [4,1,1,2,1] => 100011101 => 4
01001111 => 00111101 => [3,1,1,1,2,1] => 100111101 => 3
01010000 => 00000101 => [6,2,1] => 100000101 => 6
01010001 => 00010101 => [4,2,2,1] => 100010101 => 5
01010010 => 00010101 => [4,2,2,1] => 100010101 => 5
01010011 => 00110101 => [3,1,2,2,1] => 100110101 => 4
01010100 => 00010101 => [4,2,2,1] => 100010101 => 5
01010101 => 01010101 => [2,2,2,2,1] => 101010101 => 4
01010110 => 00101011 => [3,2,2,1,1] => 100101011 => 4
01010111 => 01010111 => [2,2,2,1,1,1] => 101010111 => 3
01011000 => 00001011 => [5,2,1,1] => 100001011 => 5
01011001 => 00101011 => [3,2,2,1,1] => 100101011 => 4
01011010 => 00101011 => [3,2,2,1,1] => 100101011 => 4
01011011 => 01011011 => [2,2,1,2,1,1] => 101011011 => 3
01011100 => 00010111 => [4,2,1,1,1] => 100010111 => 4
01011101 => 01010111 => [2,2,2,1,1,1] => 101010111 => 3
01011110 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
01011111 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 2
01100000 => 00000011 => [7,1,1] => 100000011 => 6
01100001 => 00001011 => [5,2,1,1] => 100001011 => 5
01100010 => 00001011 => [5,2,1,1] => 100001011 => 5
01100011 => 00011011 => [4,1,2,1,1] => 100011011 => 4
01100100 => 00001011 => [5,2,1,1] => 100001011 => 5
01100101 => 00101011 => [3,2,2,1,1] => 100101011 => 4
01100110 => 00011011 => [4,1,2,1,1] => 100011011 => 4
01100111 => 00111011 => [3,1,1,2,1,1] => 100111011 => 3
01101000 => 00001011 => [5,2,1,1] => 100001011 => 5
01101001 => 00101011 => [3,2,2,1,1] => 100101011 => 4
01101010 => 00101011 => [3,2,2,1,1] => 100101011 => 4
01101011 => 01011011 => [2,2,1,2,1,1] => 101011011 => 3
01101100 => 00011011 => [4,1,2,1,1] => 100011011 => 4
01101101 => 01011011 => [2,2,1,2,1,1] => 101011011 => 3
01101110 => 00110111 => [3,1,2,1,1,1] => 100110111 => 3
01101111 => 01101111 => [2,1,2,1,1,1,1] => 101101111 => 2
01110000 => 00000111 => [6,1,1,1] => 100000111 => 5
01110001 => 00010111 => [4,2,1,1,1] => 100010111 => 4
01110010 => 00010111 => [4,2,1,1,1] => 100010111 => 4
01110011 => 00110111 => [3,1,2,1,1,1] => 100110111 => 3
01110100 => 00010111 => [4,2,1,1,1] => 100010111 => 4
01110101 => 01010111 => [2,2,2,1,1,1] => 101010111 => 3
01110110 => 00110111 => [3,1,2,1,1,1] => 100110111 => 3
01110111 => 01110111 => [2,1,1,2,1,1,1] => 101110111 => 2
01111000 => 00001111 => [5,1,1,1,1] => 100001111 => 4
01111001 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
01111010 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
01111011 => 01101111 => [2,1,2,1,1,1,1] => 101101111 => 2
01111100 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
01111101 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 2
01111110 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
01111111 => 01111111 => [2,1,1,1,1,1,1,1] => 101111111 => 1
10000000 => 00000001 => [8,1] => 100000001 => 7
10000001 => 00000011 => [7,1,1] => 100000011 => 6
10000010 => 00000011 => [7,1,1] => 100000011 => 6
10000011 => 00000111 => [6,1,1,1] => 100000111 => 5
10000100 => 00000011 => [7,1,1] => 100000011 => 6
10000101 => 00001011 => [5,2,1,1] => 100001011 => 5
10000110 => 00000111 => [6,1,1,1] => 100000111 => 5
10000111 => 00001111 => [5,1,1,1,1] => 100001111 => 4
10001000 => 00000011 => [7,1,1] => 100000011 => 6
10001001 => 00010011 => [4,3,1,1] => 100010011 => 5
10001010 => 00001011 => [5,2,1,1] => 100001011 => 5
10001011 => 00010111 => [4,2,1,1,1] => 100010111 => 4
10001100 => 00000111 => [6,1,1,1] => 100000111 => 5
10001101 => 00011011 => [4,1,2,1,1] => 100011011 => 4
10001110 => 00001111 => [5,1,1,1,1] => 100001111 => 4
10001111 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
10010000 => 00000011 => [7,1,1] => 100000011 => 6
10010001 => 00010011 => [4,3,1,1] => 100010011 => 5
10010010 => 00010011 => [4,3,1,1] => 100010011 => 5
10010011 => 00100111 => [3,3,1,1,1] => 100100111 => 4
10010100 => 00001011 => [5,2,1,1] => 100001011 => 5
10010101 => 00101011 => [3,2,2,1,1] => 100101011 => 4
10010110 => 00010111 => [4,2,1,1,1] => 100010111 => 4
10010111 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
10011000 => 00000111 => [6,1,1,1] => 100000111 => 5
10011001 => 00100111 => [3,3,1,1,1] => 100100111 => 4
10011010 => 00011011 => [4,1,2,1,1] => 100011011 => 4
10011011 => 00110111 => [3,1,2,1,1,1] => 100110111 => 3
10011100 => 00001111 => [5,1,1,1,1] => 100001111 => 4
10011101 => 00111011 => [3,1,1,2,1,1] => 100111011 => 3
10011110 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
10011111 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
10100000 => 00000011 => [7,1,1] => 100000011 => 6
10100001 => 00001011 => [5,2,1,1] => 100001011 => 5
10100010 => 00001011 => [5,2,1,1] => 100001011 => 5
10100011 => 00011011 => [4,1,2,1,1] => 100011011 => 4
10100100 => 00001011 => [5,2,1,1] => 100001011 => 5
10100101 => 00101011 => [3,2,2,1,1] => 100101011 => 4
10100110 => 00011011 => [4,1,2,1,1] => 100011011 => 4
10100111 => 00111011 => [3,1,1,2,1,1] => 100111011 => 3
10101000 => 00001011 => [5,2,1,1] => 100001011 => 5
10101001 => 00101011 => [3,2,2,1,1] => 100101011 => 4
10101010 => 00101011 => [3,2,2,1,1] => 100101011 => 4
10101011 => 01010111 => [2,2,2,1,1,1] => 101010111 => 3
10101100 => 00010111 => [4,2,1,1,1] => 100010111 => 4
10101101 => 01010111 => [2,2,2,1,1,1] => 101010111 => 3
10101110 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
10101111 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 2
10110000 => 00000111 => [6,1,1,1] => 100000111 => 5
10110001 => 00010111 => [4,2,1,1,1] => 100010111 => 4
10110010 => 00010111 => [4,2,1,1,1] => 100010111 => 4
10110011 => 00110111 => [3,1,2,1,1,1] => 100110111 => 3
10110100 => 00010111 => [4,2,1,1,1] => 100010111 => 4
10110101 => 01010111 => [2,2,2,1,1,1] => 101010111 => 3
10110110 => 00110111 => [3,1,2,1,1,1] => 100110111 => 3
10110111 => 01101111 => [2,1,2,1,1,1,1] => 101101111 => 2
10111000 => 00001111 => [5,1,1,1,1] => 100001111 => 4
10111001 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
10111010 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
10111011 => 01101111 => [2,1,2,1,1,1,1] => 101101111 => 2
10111100 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
10111101 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 2
10111110 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
10111111 => 01111111 => [2,1,1,1,1,1,1,1] => 101111111 => 1
11000000 => 00000011 => [7,1,1] => 100000011 => 6
11000001 => 00000111 => [6,1,1,1] => 100000111 => 5
11000010 => 00000111 => [6,1,1,1] => 100000111 => 5
11000011 => 00001111 => [5,1,1,1,1] => 100001111 => 4
11000100 => 00000111 => [6,1,1,1] => 100000111 => 5
11000101 => 00010111 => [4,2,1,1,1] => 100010111 => 4
11000110 => 00001111 => [5,1,1,1,1] => 100001111 => 4
11000111 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
11001000 => 00000111 => [6,1,1,1] => 100000111 => 5
11001001 => 00100111 => [3,3,1,1,1] => 100100111 => 4
11001010 => 00010111 => [4,2,1,1,1] => 100010111 => 4
11001011 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
11001100 => 00001111 => [5,1,1,1,1] => 100001111 => 4
11001101 => 00110111 => [3,1,2,1,1,1] => 100110111 => 3
11001110 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
11001111 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
11010000 => 00000111 => [6,1,1,1] => 100000111 => 5
11010001 => 00010111 => [4,2,1,1,1] => 100010111 => 4
11010010 => 00010111 => [4,2,1,1,1] => 100010111 => 4
11010011 => 00110111 => [3,1,2,1,1,1] => 100110111 => 3
11010100 => 00010111 => [4,2,1,1,1] => 100010111 => 4
11010101 => 01010111 => [2,2,2,1,1,1] => 101010111 => 3
11010110 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
11010111 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 2
11011000 => 00001111 => [5,1,1,1,1] => 100001111 => 4
11011001 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
11011010 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
11011011 => 01101111 => [2,1,2,1,1,1,1] => 101101111 => 2
11011100 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
11011101 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 2
11011110 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
11011111 => 01111111 => [2,1,1,1,1,1,1,1] => 101111111 => 1
11100000 => 00000111 => [6,1,1,1] => 100000111 => 5
11100001 => 00001111 => [5,1,1,1,1] => 100001111 => 4
11100010 => 00001111 => [5,1,1,1,1] => 100001111 => 4
11100011 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
11100100 => 00001111 => [5,1,1,1,1] => 100001111 => 4
11100101 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
11100110 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
11100111 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
11101000 => 00001111 => [5,1,1,1,1] => 100001111 => 4
11101001 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
11101010 => 00101111 => [3,2,1,1,1,1] => 100101111 => 3
11101011 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 2
11101100 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
11101101 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 2
11101110 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
11101111 => 01111111 => [2,1,1,1,1,1,1,1] => 101111111 => 1
11110000 => 00001111 => [5,1,1,1,1] => 100001111 => 4
11110001 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
11110010 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
11110011 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
11110100 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
11110101 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 2
11110110 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
11110111 => 01111111 => [2,1,1,1,1,1,1,1] => 101111111 => 1
11111000 => 00011111 => [4,1,1,1,1,1] => 100011111 => 3
11111001 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
11111010 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
11111011 => 01111111 => [2,1,1,1,1,1,1,1] => 101111111 => 1
11111100 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 2
11111101 => 01111111 => [2,1,1,1,1,1,1,1] => 101111111 => 1
11111110 => 01111111 => [2,1,1,1,1,1,1,1] => 101111111 => 1
11111111 => 11111111 => [1,1,1,1,1,1,1,1,1] => 111111111 => 0
=> => [1] => 1 => 0
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Description
The index of a given binary word in the lex-order among all its cyclic shifts.
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 $0$.
Map
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.