Identifier
Values
0 => 0 => [2] => 2
1 => 1 => [1,1] => 1
00 => 00 => [3] => 3
01 => 10 => [1,2] => 2
10 => 01 => [2,1] => 1
11 => 11 => [1,1,1] => 1
000 => 000 => [4] => 4
001 => 100 => [1,3] => 3
010 => 010 => [2,2] => 2
011 => 110 => [1,1,2] => 2
100 => 001 => [3,1] => 1
101 => 101 => [1,2,1] => 1
110 => 011 => [2,1,1] => 1
111 => 111 => [1,1,1,1] => 1
0000 => 0000 => [5] => 5
0001 => 1000 => [1,4] => 4
0010 => 0100 => [2,3] => 3
0011 => 1100 => [1,1,3] => 3
0100 => 0010 => [3,2] => 2
0101 => 1010 => [1,2,2] => 2
0110 => 0110 => [2,1,2] => 2
0111 => 1110 => [1,1,1,2] => 2
1000 => 0001 => [4,1] => 1
1001 => 1001 => [1,3,1] => 1
1010 => 0101 => [2,2,1] => 1
1011 => 1101 => [1,1,2,1] => 1
1100 => 0011 => [3,1,1] => 1
1101 => 1011 => [1,2,1,1] => 1
1110 => 0111 => [2,1,1,1] => 1
1111 => 1111 => [1,1,1,1,1] => 1
00000 => 00000 => [6] => 6
00001 => 10000 => [1,5] => 5
00010 => 01000 => [2,4] => 4
00011 => 11000 => [1,1,4] => 4
00100 => 00100 => [3,3] => 3
00101 => 10100 => [1,2,3] => 3
00110 => 01100 => [2,1,3] => 3
00111 => 11100 => [1,1,1,3] => 3
01000 => 00010 => [4,2] => 2
01001 => 10010 => [1,3,2] => 2
01010 => 01010 => [2,2,2] => 2
01011 => 11010 => [1,1,2,2] => 2
01100 => 00110 => [3,1,2] => 2
01101 => 10110 => [1,2,1,2] => 2
01110 => 01110 => [2,1,1,2] => 2
01111 => 11110 => [1,1,1,1,2] => 2
10000 => 00001 => [5,1] => 1
10001 => 10001 => [1,4,1] => 1
10010 => 01001 => [2,3,1] => 1
10011 => 11001 => [1,1,3,1] => 1
10100 => 00101 => [3,2,1] => 1
10101 => 10101 => [1,2,2,1] => 1
10110 => 01101 => [2,1,2,1] => 1
10111 => 11101 => [1,1,1,2,1] => 1
11000 => 00011 => [4,1,1] => 1
11001 => 10011 => [1,3,1,1] => 1
11010 => 01011 => [2,2,1,1] => 1
11011 => 11011 => [1,1,2,1,1] => 1
11100 => 00111 => [3,1,1,1] => 1
11101 => 10111 => [1,2,1,1,1] => 1
11110 => 01111 => [2,1,1,1,1] => 1
11111 => 11111 => [1,1,1,1,1,1] => 1
000000 => 000000 => [7] => 7
000001 => 100000 => [1,6] => 6
000010 => 010000 => [2,5] => 5
000011 => 110000 => [1,1,5] => 5
000100 => 001000 => [3,4] => 4
000101 => 101000 => [1,2,4] => 4
000110 => 011000 => [2,1,4] => 4
000111 => 111000 => [1,1,1,4] => 4
001000 => 000100 => [4,3] => 3
001001 => 100100 => [1,3,3] => 3
001010 => 010100 => [2,2,3] => 3
001011 => 110100 => [1,1,2,3] => 3
001100 => 001100 => [3,1,3] => 3
001101 => 101100 => [1,2,1,3] => 3
001110 => 011100 => [2,1,1,3] => 3
001111 => 111100 => [1,1,1,1,3] => 3
010000 => 000010 => [5,2] => 2
010001 => 100010 => [1,4,2] => 2
010010 => 010010 => [2,3,2] => 2
010011 => 110010 => [1,1,3,2] => 2
010100 => 001010 => [3,2,2] => 2
010101 => 101010 => [1,2,2,2] => 2
010110 => 011010 => [2,1,2,2] => 2
010111 => 111010 => [1,1,1,2,2] => 2
011000 => 000110 => [4,1,2] => 2
011001 => 100110 => [1,3,1,2] => 2
011010 => 010110 => [2,2,1,2] => 2
011011 => 110110 => [1,1,2,1,2] => 2
011100 => 001110 => [3,1,1,2] => 2
011101 => 101110 => [1,2,1,1,2] => 2
011110 => 011110 => [2,1,1,1,2] => 2
011111 => 111110 => [1,1,1,1,1,2] => 2
100000 => 000001 => [6,1] => 1
100001 => 100001 => [1,5,1] => 1
100010 => 010001 => [2,4,1] => 1
100011 => 110001 => [1,1,4,1] => 1
100100 => 001001 => [3,3,1] => 1
100101 => 101001 => [1,2,3,1] => 1
100110 => 011001 => [2,1,3,1] => 1
>>> Load all 362 entries. <<<
100111 => 111001 => [1,1,1,3,1] => 1
101000 => 000101 => [4,2,1] => 1
101001 => 100101 => [1,3,2,1] => 1
101010 => 010101 => [2,2,2,1] => 1
101011 => 110101 => [1,1,2,2,1] => 1
101100 => 001101 => [3,1,2,1] => 1
101101 => 101101 => [1,2,1,2,1] => 1
101110 => 011101 => [2,1,1,2,1] => 1
101111 => 111101 => [1,1,1,1,2,1] => 1
110000 => 000011 => [5,1,1] => 1
110001 => 100011 => [1,4,1,1] => 1
110010 => 010011 => [2,3,1,1] => 1
110011 => 110011 => [1,1,3,1,1] => 1
110100 => 001011 => [3,2,1,1] => 1
110101 => 101011 => [1,2,2,1,1] => 1
110110 => 011011 => [2,1,2,1,1] => 1
110111 => 111011 => [1,1,1,2,1,1] => 1
111000 => 000111 => [4,1,1,1] => 1
111001 => 100111 => [1,3,1,1,1] => 1
111010 => 010111 => [2,2,1,1,1] => 1
111011 => 110111 => [1,1,2,1,1,1] => 1
111100 => 001111 => [3,1,1,1,1] => 1
111101 => 101111 => [1,2,1,1,1,1] => 1
111110 => 011111 => [2,1,1,1,1,1] => 1
111111 => 111111 => [1,1,1,1,1,1,1] => 1
0000001 => 1000000 => [1,7] => 7
0001000 => 0001000 => [4,4] => 4
0001101 => 1011000 => [1,2,1,4] => 4
0010001 => 1000100 => [1,4,3] => 3
0010010 => 0100100 => [2,3,3] => 3
0010011 => 1100100 => [1,1,3,3] => 3
0010100 => 0010100 => [3,2,3] => 3
0010101 => 1010100 => [1,2,2,3] => 3
0010110 => 0110100 => [2,1,2,3] => 3
0011001 => 1001100 => [1,3,1,3] => 3
0011010 => 0101100 => [2,2,1,3] => 3
0011100 => 0011100 => [3,1,1,3] => 3
0100001 => 1000010 => [1,5,2] => 2
0100010 => 0100010 => [2,4,2] => 2
0100100 => 0010010 => [3,3,2] => 2
0100101 => 1010010 => [1,2,3,2] => 2
0100110 => 0110010 => [2,1,3,2] => 2
0100111 => 1110010 => [1,1,1,3,2] => 2
0101001 => 1001010 => [1,3,2,2] => 2
0101010 => 0101010 => [2,2,2,2] => 2
0101011 => 1101010 => [1,1,2,2,2] => 2
0101100 => 0011010 => [3,1,2,2] => 2
0101101 => 1011010 => [1,2,1,2,2] => 2
0101110 => 0111010 => [2,1,1,2,2] => 2
0101111 => 1111010 => [1,1,1,1,2,2] => 2
0110001 => 1000110 => [1,4,1,2] => 2
0110010 => 0100110 => [2,3,1,2] => 2
0110011 => 1100110 => [1,1,3,1,2] => 2
0110100 => 0010110 => [3,2,1,2] => 2
0110101 => 1010110 => [1,2,2,1,2] => 2
0110110 => 0110110 => [2,1,2,1,2] => 2
0110111 => 1110110 => [1,1,1,2,1,2] => 2
0111001 => 1001110 => [1,3,1,1,2] => 2
0111010 => 0101110 => [2,2,1,1,2] => 2
0111011 => 1101110 => [1,1,2,1,1,2] => 2
0111101 => 1011110 => [1,2,1,1,1,2] => 2
0111110 => 0111110 => [2,1,1,1,1,2] => 2
1000000 => 0000001 => [7,1] => 1
1000001 => 1000001 => [1,6,1] => 1
1000011 => 1100001 => [1,1,5,1] => 1
1000100 => 0010001 => [3,4,1] => 1
1000101 => 1010001 => [1,2,4,1] => 1
1000110 => 0110001 => [2,1,4,1] => 1
1001000 => 0001001 => [4,3,1] => 1
1001001 => 1001001 => [1,3,3,1] => 1
1001010 => 0101001 => [2,2,3,1] => 1
1001011 => 1101001 => [1,1,2,3,1] => 1
1001100 => 0011001 => [3,1,3,1] => 1
1001101 => 1011001 => [1,2,1,3,1] => 1
1001110 => 0111001 => [2,1,1,3,1] => 1
1001111 => 1111001 => [1,1,1,1,3,1] => 1
1010000 => 0000101 => [5,2,1] => 1
1010001 => 1000101 => [1,4,2,1] => 1
1010010 => 0100101 => [2,3,2,1] => 1
1010011 => 1100101 => [1,1,3,2,1] => 1
1010100 => 0010101 => [3,2,2,1] => 1
1010101 => 1010101 => [1,2,2,2,1] => 1
1010110 => 0110101 => [2,1,2,2,1] => 1
1010111 => 1110101 => [1,1,1,2,2,1] => 1
1011000 => 0001101 => [4,1,2,1] => 1
1011001 => 1001101 => [1,3,1,2,1] => 1
1011010 => 0101101 => [2,2,1,2,1] => 1
1011011 => 1101101 => [1,1,2,1,2,1] => 1
1011101 => 1011101 => [1,2,1,1,2,1] => 1
1011110 => 0111101 => [2,1,1,1,2,1] => 1
1011111 => 1111101 => [1,1,1,1,1,2,1] => 1
1100000 => 0000011 => [6,1,1] => 1
1100001 => 1000011 => [1,5,1,1] => 1
1100100 => 0010011 => [3,3,1,1] => 1
1100101 => 1010011 => [1,2,3,1,1] => 1
1100110 => 0110011 => [2,1,3,1,1] => 1
1100111 => 1110011 => [1,1,1,3,1,1] => 1
1101001 => 1001011 => [1,3,2,1,1] => 1
1101010 => 0101011 => [2,2,2,1,1] => 1
1101011 => 1101011 => [1,1,2,2,1,1] => 1
1101101 => 1011011 => [1,2,1,2,1,1] => 1
1101110 => 0111011 => [2,1,1,2,1,1] => 1
1101111 => 1111011 => [1,1,1,1,2,1,1] => 1
1110000 => 0000111 => [5,1,1,1] => 1
1110010 => 0100111 => [2,3,1,1,1] => 1
1110011 => 1100111 => [1,1,3,1,1,1] => 1
1110101 => 1010111 => [1,2,2,1,1,1] => 1
1110110 => 0110111 => [2,1,2,1,1,1] => 1
1110111 => 1110111 => [1,1,1,2,1,1,1] => 1
1111001 => 1001111 => [1,3,1,1,1,1] => 1
1111010 => 0101111 => [2,2,1,1,1,1] => 1
1111011 => 1101111 => [1,1,2,1,1,1,1] => 1
1111101 => 1011111 => [1,2,1,1,1,1,1] => 1
1111111 => 1111111 => [1,1,1,1,1,1,1,1] => 1
00000001 => 10000000 => [1,8] => 8
00110001 => 10001100 => [1,4,1,3] => 3
01000001 => 10000010 => [1,6,2] => 2
01010001 => 10001010 => [1,4,2,2] => 2
01100001 => 10000110 => [1,5,1,2] => 2
10000000 => 00000001 => [8,1] => 1
10000001 => 10000001 => [1,7,1] => 1
10000011 => 11000001 => [1,1,6,1] => 1
10000101 => 10100001 => [1,2,5,1] => 1
10000110 => 01100001 => [2,1,5,1] => 1
10001001 => 10010001 => [1,3,4,1] => 1
10001010 => 01010001 => [2,2,4,1] => 1
10001100 => 00110001 => [3,1,4,1] => 1
10001111 => 11110001 => [1,1,1,1,4,1] => 1
10010001 => 10001001 => [1,4,3,1] => 1
10010111 => 11101001 => [1,1,1,2,3,1] => 1
10011011 => 11011001 => [1,1,2,1,3,1] => 1
10011101 => 10111001 => [1,2,1,1,3,1] => 1
10100000 => 00000101 => [6,2,1] => 1
10100001 => 10000101 => [1,5,2,1] => 1
10101101 => 10110101 => [1,2,1,2,2,1] => 1
10110101 => 10101101 => [1,2,2,1,2,1] => 1
10111001 => 10011101 => [1,3,1,1,2,1] => 1
11000000 => 00000011 => [7,1,1] => 1
11000001 => 10000011 => [1,6,1,1] => 1
11011001 => 10011011 => [1,3,1,2,1,1] => 1
11101001 => 10010111 => [1,3,2,1,1,1] => 1
11110001 => 10001111 => [1,4,1,1,1,1] => 1
000000001 => 100000000 => [1,9] => 9
000010000 => 000010000 => [5,5] => 5
000100011 => 110001000 => [1,1,4,4] => 4
000100110 => 011001000 => [2,1,3,4] => 4
000101100 => 001101000 => [3,1,2,4] => 4
000111000 => 000111000 => [4,1,1,4] => 4
001001010 => 010100100 => [2,2,3,3] => 3
001001111 => 111100100 => [1,1,1,1,3,3] => 3
001010100 => 001010100 => [3,2,2,3] => 3
001011011 => 110110100 => [1,1,2,1,2,3] => 3
001011110 => 011110100 => [2,1,1,1,2,3] => 3
001101000 => 000101100 => [4,2,1,3] => 3
001110011 => 110011100 => [1,1,3,1,1,3] => 3
001110110 => 011011100 => [2,1,2,1,1,3] => 3
001111100 => 001111100 => [3,1,1,1,1,3] => 3
010100100 => 001001010 => [3,3,2,2] => 2
010101011 => 110101010 => [1,1,2,2,2,2] => 2
010101110 => 011101010 => [2,1,1,2,2,2] => 2
010111010 => 010111010 => [2,2,1,1,2,2] => 2
010111111 => 111111010 => [1,1,1,1,1,1,2,2] => 2
011000001 => 100000110 => [1,6,1,2] => 2
011001000 => 000100110 => [4,3,1,2] => 2
011010011 => 110010110 => [1,1,3,2,1,2] => 2
011010110 => 011010110 => [2,1,2,2,1,2] => 2
011011100 => 001110110 => [3,1,1,2,1,2] => 2
011101010 => 010101110 => [2,2,2,1,1,2] => 2
011101111 => 111101110 => [1,1,1,1,2,1,1,2] => 2
011110100 => 001011110 => [3,2,1,1,1,2] => 2
011111011 => 110111110 => [1,1,2,1,1,1,1,2] => 2
011111110 => 011111110 => [2,1,1,1,1,1,1,2] => 2
100000000 => 000000001 => [9,1] => 1
100000001 => 100000001 => [1,8,1] => 1
100000011 => 110000001 => [1,1,7,1] => 1
100000101 => 101000001 => [1,2,6,1] => 1
100000110 => 011000001 => [2,1,6,1] => 1
100001001 => 100100001 => [1,3,5,1] => 1
100001111 => 111100001 => [1,1,1,1,5,1] => 1
100010001 => 100010001 => [1,4,4,1] => 1
100011101 => 101110001 => [1,2,1,1,4,1] => 1
100100001 => 100001001 => [1,5,3,1] => 1
100111001 => 100111001 => [1,3,1,1,3,1] => 1
101000001 => 100000101 => [1,6,2,1] => 1
101110001 => 100011101 => [1,4,1,1,2,1] => 1
110000000 => 000000011 => [8,1,1] => 1
110000001 => 100000011 => [1,7,1,1] => 1
110001000 => 000100011 => [4,4,1,1] => 1
110010011 => 110010011 => [1,1,3,3,1,1] => 1
110010110 => 011010011 => [2,1,2,3,1,1] => 1
110011100 => 001110011 => [3,1,1,3,1,1] => 1
110101010 => 010101011 => [2,2,2,2,1,1] => 1
110101111 => 111101011 => [1,1,1,1,2,2,1,1] => 1
110110100 => 001011011 => [3,2,1,2,1,1] => 1
110111011 => 110111011 => [1,1,2,1,1,2,1,1] => 1
110111110 => 011111011 => [2,1,1,1,1,2,1,1] => 1
111100001 => 100001111 => [1,5,1,1,1,1] => 1
111100100 => 001001111 => [3,3,1,1,1,1] => 1
111101011 => 110101111 => [1,1,2,2,1,1,1,1] => 1
111101110 => 011101111 => [2,1,1,2,1,1,1,1] => 1
111111010 => 010111111 => [2,2,1,1,1,1,1,1] => 1
111111111 => 111111111 => [1,1,1,1,1,1,1,1,1,1] => 1
1100000001 => 1000000011 => [1,8,1,1] => 1
1010000001 => 1000000101 => [1,7,2,1] => 1
1001000001 => 1000001001 => [1,6,3,1] => 1
1000000101 => 1010000001 => [1,2,7,1] => 1
1000000011 => 1100000001 => [1,1,8,1] => 1
1000000000 => 0000000001 => [10,1] => 1
11011111110 => 01111111011 => [2,1,1,1,1,1,1,2,1,1] => 1
11110111110 => 01111101111 => [2,1,1,1,1,2,1,1,1,1] => 1
11111101110 => 01110111111 => [2,1,1,2,1,1,1,1,1,1] => 1
11010101110 => 01110101011 => [2,1,1,2,2,2,1,1] => 1
11111111010 => 01011111111 => [2,2,1,1,1,1,1,1,1,1] => 1
=> => [1] => 1
0000000001 => 1000000000 => [1,10] => 10
11010100100 => 00100101011 => [3,3,2,2,1,1] => 1
11001010100 => 00101010011 => [3,2,2,3,1,1] => 1
00101010011 => 11001010100 => [1,1,3,2,2,3] => 3
00100101011 => 11010100100 => [1,1,2,2,3,3] => 3
01111111110 => 01111111110 => [2,1,1,1,1,1,1,1,1,2] => 2
01010101010 => 01010101010 => [2,2,2,2,2,2] => 2
01010001000 => 00010001010 => [4,4,2,2] => 2
00100100100 => 00100100100 => [3,3,3,3] => 3
00101001000 => 00010010100 => [4,3,2,3] => 3
00010001010 => 01010001000 => [2,2,4,4] => 4
00010010100 => 00101001000 => [3,2,3,4] => 4
00010101000 => 00010101000 => [4,2,2,4] => 4
00000100000 => 00000100000 => [6,6] => 6
01011111111 => 11111111010 => [1,1,1,1,1,1,1,1,2,2] => 2
01111111011 => 11011111110 => [1,1,2,1,1,1,1,1,1,2] => 2
11111111111 => 11111111111 => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
01010111011 => 11011101010 => [1,1,2,1,1,2,2,2] => 2
01011101110 => 01110111010 => [2,1,1,2,1,1,2,2] => 2
01011101011 => 11010111010 => [1,1,2,2,1,1,2,2] => 2
01101110110 => 01101110110 => [2,1,2,1,1,2,1,2] => 2
01101011011 => 11011010110 => [1,1,2,1,2,2,1,2] => 2
01110111010 => 01011101110 => [2,2,1,1,2,1,1,2] => 2
01110101110 => 01110101110 => [2,1,1,2,2,1,1,2] => 2
01110101011 => 11010101110 => [1,1,2,2,2,1,1,2] => 2
01111101111 => 11110111110 => [1,1,1,1,2,1,1,1,1,2] => 2
11011101010 => 01010111011 => [2,2,2,1,1,2,1,1] => 1
11011111011 => 11011111011 => [1,1,2,1,1,1,1,2,1,1] => 1
11011010110 => 01101011011 => [2,1,2,2,1,2,1,1] => 1
11010111010 => 01011101011 => [2,2,1,1,2,2,1,1] => 1
11010101011 => 11010101011 => [1,1,2,2,2,2,1,1] => 1
11011101111 => 11110111011 => [1,1,1,1,2,1,1,2,1,1] => 1
11110111011 => 11011101111 => [1,1,2,1,1,2,1,1,1,1] => 1
11110101111 => 11110101111 => [1,1,1,1,2,2,1,1,1,1] => 1
00111111100 => 00111111100 => [3,1,1,1,1,1,1,3] => 3
11110101010 => 01010101111 => [2,2,2,2,1,1,1,1] => 1
01110111111 => 11111101110 => [1,1,1,1,1,1,2,1,1,2] => 2
11110001000 => 00010001111 => [4,4,1,1,1,1] => 1
11000111000 => 00011100011 => [4,1,1,4,1,1] => 1
11000100011 => 11000100011 => [1,1,4,4,1,1] => 1
00011111000 => 00011111000 => [4,1,1,1,1,4] => 4
00011100011 => 11000111000 => [1,1,4,1,1,4] => 4
00010001111 => 11110001000 => [1,1,1,1,4,4] => 4
01011111010 => 01011111010 => [2,2,1,1,1,1,2,2] => 2
00101111011 => 11011110100 => [1,1,2,1,1,1,2,3] => 3
00101101010 => 01010110100 => [2,2,2,1,2,3] => 3
00101010110 => 01101010100 => [2,1,2,2,2,3] => 3
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Description
The last part of an integer composition.
Map
reverse
Description
Return the reversal of a binary word.
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.