Identifier
-
Mp00224:
Binary words
—runsort⟶
Binary words
St001419: Binary words ⟶ ℤ
Values
0 => 0 => 0
1 => 1 => 1
00 => 00 => 0
01 => 01 => 1
10 => 01 => 1
11 => 11 => 2
000 => 000 => 0
001 => 001 => 1
010 => 001 => 1
011 => 011 => 2
100 => 001 => 1
101 => 011 => 2
110 => 011 => 2
111 => 111 => 3
0000 => 0000 => 0
0001 => 0001 => 1
0010 => 0001 => 1
0011 => 0011 => 2
0100 => 0001 => 1
0101 => 0101 => 3
0110 => 0011 => 2
0111 => 0111 => 3
1000 => 0001 => 1
1001 => 0011 => 2
1010 => 0011 => 2
1011 => 0111 => 3
1100 => 0011 => 2
1101 => 0111 => 3
1110 => 0111 => 3
1111 => 1111 => 4
00000 => 00000 => 0
00001 => 00001 => 1
00010 => 00001 => 1
00011 => 00011 => 2
00100 => 00001 => 1
00101 => 00101 => 3
00110 => 00011 => 2
00111 => 00111 => 3
01000 => 00001 => 1
01001 => 00101 => 3
01010 => 00101 => 3
01011 => 01011 => 3
01100 => 00011 => 2
01101 => 01011 => 3
01110 => 00111 => 3
01111 => 01111 => 4
10000 => 00001 => 1
10001 => 00011 => 2
10010 => 00011 => 2
10011 => 00111 => 3
10100 => 00011 => 2
10101 => 01011 => 3
10110 => 00111 => 3
10111 => 01111 => 4
11000 => 00011 => 2
11001 => 00111 => 3
11010 => 00111 => 3
11011 => 01111 => 4
11100 => 00111 => 3
11101 => 01111 => 4
11110 => 01111 => 4
11111 => 11111 => 5
000000 => 000000 => 0
000001 => 000001 => 1
000010 => 000001 => 1
000011 => 000011 => 2
000100 => 000001 => 1
000101 => 000101 => 3
000110 => 000011 => 2
000111 => 000111 => 3
001000 => 000001 => 1
001001 => 001001 => 4
001010 => 000101 => 3
001011 => 001011 => 3
001100 => 000011 => 2
001101 => 001101 => 3
001110 => 000111 => 3
001111 => 001111 => 4
010000 => 000001 => 1
010001 => 000101 => 3
010010 => 000101 => 3
010011 => 001101 => 3
010100 => 000101 => 3
010101 => 010101 => 5
010110 => 001011 => 3
010111 => 010111 => 3
011000 => 000011 => 2
011001 => 001011 => 3
011010 => 001011 => 3
011011 => 011011 => 5
011100 => 000111 => 3
011101 => 010111 => 3
011110 => 001111 => 4
011111 => 011111 => 5
100000 => 000001 => 1
100001 => 000011 => 2
100010 => 000011 => 2
100011 => 000111 => 3
100100 => 000011 => 2
100101 => 001011 => 3
100110 => 000111 => 3
>>> Load all 1022 entries. <<<100111 => 001111 => 4
101000 => 000011 => 2
101001 => 001011 => 3
101010 => 001011 => 3
101011 => 010111 => 3
101100 => 000111 => 3
101101 => 010111 => 3
101110 => 001111 => 4
101111 => 011111 => 5
110000 => 000011 => 2
110001 => 000111 => 3
110010 => 000111 => 3
110011 => 001111 => 4
110100 => 000111 => 3
110101 => 010111 => 3
110110 => 001111 => 4
110111 => 011111 => 5
111000 => 000111 => 3
111001 => 001111 => 4
111010 => 001111 => 4
111011 => 011111 => 5
111100 => 001111 => 4
111101 => 011111 => 5
111110 => 011111 => 5
111111 => 111111 => 6
0000000 => 0000000 => 0
0000001 => 0000001 => 1
0000010 => 0000001 => 1
0000011 => 0000011 => 2
0000100 => 0000001 => 1
0000101 => 0000101 => 3
0000110 => 0000011 => 2
0000111 => 0000111 => 3
0001000 => 0000001 => 1
0001001 => 0001001 => 4
0001010 => 0000101 => 3
0001011 => 0001011 => 3
0001100 => 0000011 => 2
0001101 => 0001101 => 3
0001110 => 0000111 => 3
0001111 => 0001111 => 4
0010000 => 0000001 => 1
0010001 => 0001001 => 4
0010010 => 0001001 => 4
0010011 => 0010011 => 4
0010100 => 0000101 => 3
0010101 => 0010101 => 5
0010110 => 0001011 => 3
0010111 => 0010111 => 3
0011000 => 0000011 => 2
0011001 => 0010011 => 4
0011010 => 0001101 => 3
0011011 => 0011011 => 5
0011100 => 0000111 => 3
0011101 => 0011101 => 3
0011110 => 0001111 => 4
0011111 => 0011111 => 5
0100000 => 0000001 => 1
0100001 => 0000101 => 3
0100010 => 0000101 => 3
0100011 => 0001101 => 3
0100100 => 0000101 => 3
0100101 => 0010101 => 5
0100110 => 0001101 => 3
0100111 => 0011101 => 3
0101000 => 0000101 => 3
0101001 => 0010101 => 5
0101010 => 0010101 => 5
0101011 => 0101011 => 5
0101100 => 0001011 => 3
0101101 => 0101011 => 5
0101110 => 0010111 => 3
0101111 => 0101111 => 4
0110000 => 0000011 => 2
0110001 => 0001011 => 3
0110010 => 0001011 => 3
0110011 => 0011011 => 5
0110100 => 0001011 => 3
0110101 => 0101011 => 5
0110110 => 0011011 => 5
0110111 => 0110111 => 5
0111000 => 0000111 => 3
0111001 => 0010111 => 3
0111010 => 0010111 => 3
0111011 => 0110111 => 5
0111100 => 0001111 => 4
0111101 => 0101111 => 4
0111110 => 0011111 => 5
0111111 => 0111111 => 6
1000000 => 0000001 => 1
1000001 => 0000011 => 2
1000010 => 0000011 => 2
1000011 => 0000111 => 3
1000100 => 0000011 => 2
1000101 => 0001011 => 3
1000110 => 0000111 => 3
1000111 => 0001111 => 4
1001000 => 0000011 => 2
1001001 => 0010011 => 4
1001010 => 0001011 => 3
1001011 => 0010111 => 3
1001100 => 0000111 => 3
1001101 => 0011011 => 5
1001110 => 0001111 => 4
1001111 => 0011111 => 5
1010000 => 0000011 => 2
1010001 => 0001011 => 3
1010010 => 0001011 => 3
1010011 => 0011011 => 5
1010100 => 0001011 => 3
1010101 => 0101011 => 5
1010110 => 0010111 => 3
1010111 => 0101111 => 4
1011000 => 0000111 => 3
1011001 => 0010111 => 3
1011010 => 0010111 => 3
1011011 => 0110111 => 5
1011100 => 0001111 => 4
1011101 => 0101111 => 4
1011110 => 0011111 => 5
1011111 => 0111111 => 6
1100000 => 0000011 => 2
1100001 => 0000111 => 3
1100010 => 0000111 => 3
1100011 => 0001111 => 4
1100100 => 0000111 => 3
1100101 => 0010111 => 3
1100110 => 0001111 => 4
1100111 => 0011111 => 5
1101000 => 0000111 => 3
1101001 => 0010111 => 3
1101010 => 0010111 => 3
1101011 => 0101111 => 4
1101100 => 0001111 => 4
1101101 => 0101111 => 4
1101110 => 0011111 => 5
1101111 => 0111111 => 6
1110000 => 0000111 => 3
1110001 => 0001111 => 4
1110010 => 0001111 => 4
1110011 => 0011111 => 5
1110100 => 0001111 => 4
1110101 => 0101111 => 4
1110110 => 0011111 => 5
1110111 => 0111111 => 6
1111000 => 0001111 => 4
1111001 => 0011111 => 5
1111010 => 0011111 => 5
1111011 => 0111111 => 6
1111100 => 0011111 => 5
1111101 => 0111111 => 6
1111110 => 0111111 => 6
1111111 => 1111111 => 7
00000000 => 00000000 => 0
00000001 => 00000001 => 1
00000010 => 00000001 => 1
00000011 => 00000011 => 2
00000100 => 00000001 => 1
00000101 => 00000101 => 3
00000110 => 00000011 => 2
00000111 => 00000111 => 3
00001000 => 00000001 => 1
00001001 => 00001001 => 4
00001010 => 00000101 => 3
00001011 => 00001011 => 3
00001100 => 00000011 => 2
00001101 => 00001101 => 3
00001110 => 00000111 => 3
00001111 => 00001111 => 4
00010000 => 00000001 => 1
00010001 => 00010001 => 5
00010010 => 00001001 => 4
00010011 => 00010011 => 4
00010100 => 00000101 => 3
00010101 => 00010101 => 5
00010110 => 00001011 => 3
00010111 => 00010111 => 3
00011000 => 00000011 => 2
00011001 => 00011001 => 4
00011010 => 00001101 => 3
00011011 => 00011011 => 5
00011100 => 00000111 => 3
00011101 => 00011101 => 3
00011110 => 00001111 => 4
00011111 => 00011111 => 5
00100000 => 00000001 => 1
00100001 => 00001001 => 4
00100010 => 00001001 => 4
00100011 => 00011001 => 4
00100100 => 00001001 => 4
00100101 => 00100101 => 4
00100110 => 00010011 => 4
00100111 => 00100111 => 4
00101000 => 00000101 => 3
00101001 => 00100101 => 4
00101010 => 00010101 => 5
00101011 => 00101011 => 5
00101100 => 00001011 => 3
00101101 => 00101011 => 5
00101110 => 00010111 => 3
00101111 => 00101111 => 4
00110000 => 00000011 => 2
00110001 => 00010011 => 4
00110010 => 00010011 => 4
00110011 => 00110011 => 6
00110100 => 00001101 => 3
00110101 => 00110101 => 5
00110110 => 00011011 => 5
00110111 => 00110111 => 5
00111000 => 00000111 => 3
00111001 => 00100111 => 4
00111010 => 00011101 => 3
00111011 => 00111011 => 5
00111100 => 00001111 => 4
00111101 => 00111101 => 4
00111110 => 00011111 => 5
00111111 => 00111111 => 6
01000000 => 00000001 => 1
01000001 => 00000101 => 3
01000010 => 00000101 => 3
01000011 => 00001101 => 3
01000100 => 00000101 => 3
01000101 => 00010101 => 5
01000110 => 00001101 => 3
01000111 => 00011101 => 3
01001000 => 00000101 => 3
01001001 => 00100101 => 4
01001010 => 00010101 => 5
01001011 => 00101011 => 5
01001100 => 00001101 => 3
01001101 => 00110101 => 5
01001110 => 00011101 => 3
01001111 => 00111101 => 4
01010000 => 00000101 => 3
01010001 => 00010101 => 5
01010010 => 00010101 => 5
01010011 => 00110101 => 5
01010100 => 00010101 => 5
01010101 => 01010101 => 7
01010110 => 00101011 => 5
01010111 => 01010111 => 5
01011000 => 00001011 => 3
01011001 => 00101011 => 5
01011010 => 00101011 => 5
01011011 => 01011011 => 6
01011100 => 00010111 => 3
01011101 => 01010111 => 5
01011110 => 00101111 => 4
01011111 => 01011111 => 5
01100000 => 00000011 => 2
01100001 => 00001011 => 3
01100010 => 00001011 => 3
01100011 => 00011011 => 5
01100100 => 00001011 => 3
01100101 => 00101011 => 5
01100110 => 00011011 => 5
01100111 => 00111011 => 5
01101000 => 00001011 => 3
01101001 => 00101011 => 5
01101010 => 00101011 => 5
01101011 => 01011011 => 6
01101100 => 00011011 => 5
01101101 => 01011011 => 6
01101110 => 00110111 => 5
01101111 => 01101111 => 5
01110000 => 00000111 => 3
01110001 => 00010111 => 3
01110010 => 00010111 => 3
01110011 => 00110111 => 5
01110100 => 00010111 => 3
01110101 => 01010111 => 5
01110110 => 00110111 => 5
01110111 => 01110111 => 7
01111000 => 00001111 => 4
01111001 => 00101111 => 4
01111010 => 00101111 => 4
01111011 => 01101111 => 5
01111100 => 00011111 => 5
01111101 => 01011111 => 5
01111110 => 00111111 => 6
01111111 => 01111111 => 7
10000000 => 00000001 => 1
10000001 => 00000011 => 2
10000010 => 00000011 => 2
10000011 => 00000111 => 3
10000100 => 00000011 => 2
10000101 => 00001011 => 3
10000110 => 00000111 => 3
10000111 => 00001111 => 4
10001000 => 00000011 => 2
10001001 => 00010011 => 4
10001010 => 00001011 => 3
10001011 => 00010111 => 3
10001100 => 00000111 => 3
10001101 => 00011011 => 5
10001110 => 00001111 => 4
10001111 => 00011111 => 5
10010000 => 00000011 => 2
10010001 => 00010011 => 4
10010010 => 00010011 => 4
10010011 => 00100111 => 4
10010100 => 00001011 => 3
10010101 => 00101011 => 5
10010110 => 00010111 => 3
10010111 => 00101111 => 4
10011000 => 00000111 => 3
10011001 => 00100111 => 4
10011010 => 00011011 => 5
10011011 => 00110111 => 5
10011100 => 00001111 => 4
10011101 => 00111011 => 5
10011110 => 00011111 => 5
10011111 => 00111111 => 6
10100000 => 00000011 => 2
10100001 => 00001011 => 3
10100010 => 00001011 => 3
10100011 => 00011011 => 5
10100100 => 00001011 => 3
10100101 => 00101011 => 5
10100110 => 00011011 => 5
10100111 => 00111011 => 5
10101000 => 00001011 => 3
10101001 => 00101011 => 5
10101010 => 00101011 => 5
10101011 => 01010111 => 5
10101100 => 00010111 => 3
10101101 => 01010111 => 5
10101110 => 00101111 => 4
10101111 => 01011111 => 5
10110000 => 00000111 => 3
10110001 => 00010111 => 3
10110010 => 00010111 => 3
10110011 => 00110111 => 5
10110100 => 00010111 => 3
10110101 => 01010111 => 5
10110110 => 00110111 => 5
10110111 => 01101111 => 5
10111000 => 00001111 => 4
10111001 => 00101111 => 4
10111010 => 00101111 => 4
10111011 => 01101111 => 5
10111100 => 00011111 => 5
10111101 => 01011111 => 5
10111110 => 00111111 => 6
10111111 => 01111111 => 7
11000000 => 00000011 => 2
11000001 => 00000111 => 3
11000010 => 00000111 => 3
11000011 => 00001111 => 4
11000100 => 00000111 => 3
11000101 => 00010111 => 3
11000110 => 00001111 => 4
11000111 => 00011111 => 5
11001000 => 00000111 => 3
11001001 => 00100111 => 4
11001010 => 00010111 => 3
11001011 => 00101111 => 4
11001100 => 00001111 => 4
11001101 => 00110111 => 5
11001110 => 00011111 => 5
11001111 => 00111111 => 6
11010000 => 00000111 => 3
11010001 => 00010111 => 3
11010010 => 00010111 => 3
11010011 => 00110111 => 5
11010100 => 00010111 => 3
11010101 => 01010111 => 5
11010110 => 00101111 => 4
11010111 => 01011111 => 5
11011000 => 00001111 => 4
11011001 => 00101111 => 4
11011010 => 00101111 => 4
11011011 => 01101111 => 5
11011100 => 00011111 => 5
11011101 => 01011111 => 5
11011110 => 00111111 => 6
11011111 => 01111111 => 7
11100000 => 00000111 => 3
11100001 => 00001111 => 4
11100010 => 00001111 => 4
11100011 => 00011111 => 5
11100100 => 00001111 => 4
11100101 => 00101111 => 4
11100110 => 00011111 => 5
11100111 => 00111111 => 6
11101000 => 00001111 => 4
11101001 => 00101111 => 4
11101010 => 00101111 => 4
11101011 => 01011111 => 5
11101100 => 00011111 => 5
11101101 => 01011111 => 5
11101110 => 00111111 => 6
11101111 => 01111111 => 7
11110000 => 00001111 => 4
11110001 => 00011111 => 5
11110010 => 00011111 => 5
11110011 => 00111111 => 6
11110100 => 00011111 => 5
11110101 => 01011111 => 5
11110110 => 00111111 => 6
11110111 => 01111111 => 7
11111000 => 00011111 => 5
11111001 => 00111111 => 6
11111010 => 00111111 => 6
11111011 => 01111111 => 7
11111100 => 00111111 => 6
11111101 => 01111111 => 7
11111110 => 01111111 => 7
11111111 => 11111111 => 8
000000000 => 000000000 => 0
000000001 => 000000001 => 1
000000010 => 000000001 => 1
000000011 => 000000011 => 2
000000100 => 000000001 => 1
000000101 => 000000101 => 3
000000110 => 000000011 => 2
000000111 => 000000111 => 3
000001000 => 000000001 => 1
000001001 => 000001001 => 4
000001010 => 000000101 => 3
000001011 => 000001011 => 3
000001100 => 000000011 => 2
000001101 => 000001101 => 3
000001110 => 000000111 => 3
000001111 => 000001111 => 4
000010000 => 000000001 => 1
000010001 => 000010001 => 5
000010010 => 000001001 => 4
000010011 => 000010011 => 4
000010100 => 000000101 => 3
000010101 => 000010101 => 5
000010110 => 000001011 => 3
000010111 => 000010111 => 3
000011000 => 000000011 => 2
000011001 => 000011001 => 4
000011010 => 000001101 => 3
000011011 => 000011011 => 5
000011100 => 000000111 => 3
000011101 => 000011101 => 3
000011110 => 000001111 => 4
000011111 => 000011111 => 5
000100000 => 000000001 => 1
000100001 => 000010001 => 5
000100010 => 000010001 => 5
000100011 => 000100011 => 5
000100100 => 000001001 => 4
000100101 => 000100101 => 4
000100110 => 000010011 => 4
000100111 => 000100111 => 4
000101000 => 000000101 => 3
000101001 => 000100101 => 4
000101010 => 000010101 => 5
000101011 => 000101011 => 5
000101100 => 000001011 => 3
000101101 => 000101011 => 5
000101110 => 000010111 => 3
000101111 => 000101111 => 4
000110000 => 000000011 => 2
000110001 => 000100011 => 5
000110010 => 000011001 => 4
000110011 => 000110011 => 6
000110100 => 000001101 => 3
000110101 => 000110101 => 5
000110110 => 000011011 => 5
000110111 => 000110111 => 5
000111000 => 000000111 => 3
000111001 => 000111001 => 4
000111010 => 000011101 => 3
000111011 => 000111011 => 5
000111100 => 000001111 => 4
000111101 => 000111101 => 4
000111110 => 000011111 => 5
000111111 => 000111111 => 6
001000000 => 000000001 => 1
001000001 => 000001001 => 4
001000010 => 000001001 => 4
001000011 => 000011001 => 4
001000100 => 000001001 => 4
001000101 => 000100101 => 4
001000110 => 000011001 => 4
001000111 => 000111001 => 4
001001000 => 000001001 => 4
001001001 => 001001001 => 7
001001010 => 000100101 => 4
001001011 => 001001011 => 4
001001100 => 000010011 => 4
001001101 => 001001101 => 4
001001110 => 000100111 => 4
001001111 => 001001111 => 4
001010000 => 000000101 => 3
001010001 => 000100101 => 4
001010010 => 000100101 => 4
001010011 => 001001101 => 4
001010100 => 000010101 => 5
001010101 => 001010101 => 7
001010110 => 000101011 => 5
001010111 => 001010111 => 5
001011000 => 000001011 => 3
001011001 => 001001011 => 4
001011010 => 000101011 => 5
001011011 => 001011011 => 6
001011100 => 000010111 => 3
001011101 => 001010111 => 5
001011110 => 000101111 => 4
001011111 => 001011111 => 5
001100000 => 000000011 => 2
001100001 => 000010011 => 4
001100010 => 000010011 => 4
001100011 => 000110011 => 6
001100100 => 000010011 => 4
001100101 => 001001101 => 4
001100110 => 000110011 => 6
001100111 => 001100111 => 6
001101000 => 000001101 => 3
001101001 => 001001101 => 4
001101010 => 000110101 => 5
001101011 => 001101011 => 7
001101100 => 000011011 => 5
001101101 => 001101011 => 7
001101110 => 000110111 => 5
001101111 => 001101111 => 5
001110000 => 000000111 => 3
001110001 => 000100111 => 4
001110010 => 000100111 => 4
001110011 => 001100111 => 6
001110100 => 000011101 => 3
001110101 => 001110101 => 5
001110110 => 000111011 => 5
001110111 => 001110111 => 7
001111000 => 000001111 => 4
001111001 => 001001111 => 4
001111010 => 000111101 => 4
001111011 => 001111011 => 5
001111100 => 000011111 => 5
001111101 => 001111101 => 5
001111110 => 000111111 => 6
001111111 => 001111111 => 7
010000000 => 000000001 => 1
010000001 => 000000101 => 3
010000010 => 000000101 => 3
010000011 => 000001101 => 3
010000100 => 000000101 => 3
010000101 => 000010101 => 5
010000110 => 000001101 => 3
010000111 => 000011101 => 3
010001000 => 000000101 => 3
010001001 => 000100101 => 4
010001010 => 000010101 => 5
010001011 => 000101011 => 5
010001100 => 000001101 => 3
010001101 => 000110101 => 5
010001110 => 000011101 => 3
010001111 => 000111101 => 4
010010000 => 000000101 => 3
010010001 => 000100101 => 4
010010010 => 000100101 => 4
010010011 => 001001101 => 4
010010100 => 000010101 => 5
010010101 => 001010101 => 7
010010110 => 000101011 => 5
010010111 => 001010111 => 5
010011000 => 000001101 => 3
010011001 => 001001101 => 4
010011010 => 000110101 => 5
010011011 => 001101011 => 7
010011100 => 000011101 => 3
010011101 => 001110101 => 5
010011110 => 000111101 => 4
010011111 => 001111101 => 5
010100000 => 000000101 => 3
010100001 => 000010101 => 5
010100010 => 000010101 => 5
010100011 => 000110101 => 5
010100100 => 000010101 => 5
010100101 => 001010101 => 7
010100110 => 000110101 => 5
010100111 => 001110101 => 5
010101000 => 000010101 => 5
010101001 => 001010101 => 7
010101010 => 001010101 => 7
010101011 => 010101011 => 7
010101100 => 000101011 => 5
010101101 => 010101011 => 7
010101110 => 001010111 => 5
010101111 => 010101111 => 5
010110000 => 000001011 => 3
010110001 => 000101011 => 5
010110010 => 000101011 => 5
010110011 => 001101011 => 7
010110100 => 000101011 => 5
010110101 => 010101011 => 7
010110110 => 001011011 => 6
010110111 => 010110111 => 6
010111000 => 000010111 => 3
010111001 => 001010111 => 5
010111010 => 001010111 => 5
010111011 => 010110111 => 6
010111100 => 000101111 => 4
010111101 => 010101111 => 5
010111110 => 001011111 => 5
010111111 => 010111111 => 6
011000000 => 000000011 => 2
011000001 => 000001011 => 3
011000010 => 000001011 => 3
011000011 => 000011011 => 5
011000100 => 000001011 => 3
011000101 => 000101011 => 5
011000110 => 000011011 => 5
011000111 => 000111011 => 5
011001000 => 000001011 => 3
011001001 => 001001011 => 4
011001010 => 000101011 => 5
011001011 => 001011011 => 6
011001100 => 000011011 => 5
011001101 => 001101011 => 7
011001110 => 000111011 => 5
011001111 => 001111011 => 5
011010000 => 000001011 => 3
011010001 => 000101011 => 5
011010010 => 000101011 => 5
011010011 => 001101011 => 7
011010100 => 000101011 => 5
011010101 => 010101011 => 7
011010110 => 001011011 => 6
011010111 => 010110111 => 6
011011000 => 000011011 => 5
011011001 => 001011011 => 6
011011010 => 001011011 => 6
011011011 => 011011011 => 8
011011100 => 000110111 => 5
011011101 => 010110111 => 6
011011110 => 001101111 => 5
011011111 => 011011111 => 5
011100000 => 000000111 => 3
011100001 => 000010111 => 3
011100010 => 000010111 => 3
011100011 => 000110111 => 5
011100100 => 000010111 => 3
011100101 => 001010111 => 5
011100110 => 000110111 => 5
011100111 => 001110111 => 7
011101000 => 000010111 => 3
011101001 => 001010111 => 5
011101010 => 001010111 => 5
011101011 => 010110111 => 6
011101100 => 000110111 => 5
011101101 => 010110111 => 6
011101110 => 001110111 => 7
011101111 => 011101111 => 7
011110000 => 000001111 => 4
011110001 => 000101111 => 4
011110010 => 000101111 => 4
011110011 => 001101111 => 5
011110100 => 000101111 => 4
011110101 => 010101111 => 5
011110110 => 001101111 => 5
011110111 => 011101111 => 7
011111000 => 000011111 => 5
011111001 => 001011111 => 5
011111010 => 001011111 => 5
011111011 => 011011111 => 5
011111100 => 000111111 => 6
011111101 => 010111111 => 6
011111110 => 001111111 => 7
011111111 => 011111111 => 8
100000000 => 000000001 => 1
100000001 => 000000011 => 2
100000010 => 000000011 => 2
100000011 => 000000111 => 3
100000100 => 000000011 => 2
100000101 => 000001011 => 3
100000110 => 000000111 => 3
100000111 => 000001111 => 4
100001000 => 000000011 => 2
100001001 => 000010011 => 4
100001010 => 000001011 => 3
100001011 => 000010111 => 3
100001100 => 000000111 => 3
100001101 => 000011011 => 5
100001110 => 000001111 => 4
100001111 => 000011111 => 5
100010000 => 000000011 => 2
100010001 => 000100011 => 5
100010010 => 000010011 => 4
100010011 => 000100111 => 4
100010100 => 000001011 => 3
100010101 => 000101011 => 5
100010110 => 000010111 => 3
100010111 => 000101111 => 4
100011000 => 000000111 => 3
100011001 => 000110011 => 6
100011010 => 000011011 => 5
100011011 => 000110111 => 5
100011100 => 000001111 => 4
100011101 => 000111011 => 5
100011110 => 000011111 => 5
100011111 => 000111111 => 6
100100000 => 000000011 => 2
100100001 => 000010011 => 4
100100010 => 000010011 => 4
100100011 => 000110011 => 6
100100100 => 000010011 => 4
100100101 => 001001011 => 4
100100110 => 000100111 => 4
100100111 => 001001111 => 4
100101000 => 000001011 => 3
100101001 => 001001011 => 4
100101010 => 000101011 => 5
100101011 => 001010111 => 5
100101100 => 000010111 => 3
100101101 => 001010111 => 5
100101110 => 000101111 => 4
100101111 => 001011111 => 5
100110000 => 000000111 => 3
100110001 => 000100111 => 4
100110010 => 000100111 => 4
100110011 => 001100111 => 6
100110100 => 000011011 => 5
100110101 => 001101011 => 7
100110110 => 000110111 => 5
100110111 => 001101111 => 5
100111000 => 000001111 => 4
100111001 => 001001111 => 4
100111010 => 000111011 => 5
100111011 => 001110111 => 7
100111100 => 000011111 => 5
100111101 => 001111011 => 5
100111110 => 000111111 => 6
100111111 => 001111111 => 7
101000000 => 000000011 => 2
101000001 => 000001011 => 3
101000010 => 000001011 => 3
101000011 => 000011011 => 5
101000100 => 000001011 => 3
101000101 => 000101011 => 5
101000110 => 000011011 => 5
101000111 => 000111011 => 5
101001000 => 000001011 => 3
101001001 => 001001011 => 4
101001010 => 000101011 => 5
101001011 => 001010111 => 5
101001100 => 000011011 => 5
101001101 => 001101011 => 7
101001110 => 000111011 => 5
101001111 => 001111011 => 5
101010000 => 000001011 => 3
101010001 => 000101011 => 5
101010010 => 000101011 => 5
101010011 => 001101011 => 7
101010100 => 000101011 => 5
101010101 => 010101011 => 7
101010110 => 001010111 => 5
101010111 => 010101111 => 5
101011000 => 000010111 => 3
101011001 => 001010111 => 5
101011010 => 001010111 => 5
101011011 => 010110111 => 6
101011100 => 000101111 => 4
101011101 => 010101111 => 5
101011110 => 001011111 => 5
101011111 => 010111111 => 6
101100000 => 000000111 => 3
101100001 => 000010111 => 3
101100010 => 000010111 => 3
101100011 => 000110111 => 5
101100100 => 000010111 => 3
101100101 => 001010111 => 5
101100110 => 000110111 => 5
101100111 => 001110111 => 7
101101000 => 000010111 => 3
101101001 => 001010111 => 5
101101010 => 001010111 => 5
101101011 => 010110111 => 6
101101100 => 000110111 => 5
101101101 => 010110111 => 6
101101110 => 001101111 => 5
101101111 => 011011111 => 5
101110000 => 000001111 => 4
101110001 => 000101111 => 4
101110010 => 000101111 => 4
101110011 => 001101111 => 5
101110100 => 000101111 => 4
101110101 => 010101111 => 5
101110110 => 001101111 => 5
101110111 => 011101111 => 7
101111000 => 000011111 => 5
101111001 => 001011111 => 5
101111010 => 001011111 => 5
101111011 => 011011111 => 5
101111100 => 000111111 => 6
101111101 => 010111111 => 6
101111110 => 001111111 => 7
101111111 => 011111111 => 8
110000000 => 000000011 => 2
110000001 => 000000111 => 3
110000010 => 000000111 => 3
110000011 => 000001111 => 4
110000100 => 000000111 => 3
110000101 => 000010111 => 3
110000110 => 000001111 => 4
110000111 => 000011111 => 5
110001000 => 000000111 => 3
110001001 => 000100111 => 4
110001010 => 000010111 => 3
110001011 => 000101111 => 4
110001100 => 000001111 => 4
110001101 => 000110111 => 5
110001110 => 000011111 => 5
110001111 => 000111111 => 6
110010000 => 000000111 => 3
110010001 => 000100111 => 4
110010010 => 000100111 => 4
110010011 => 001001111 => 4
110010100 => 000010111 => 3
110010101 => 001010111 => 5
110010110 => 000101111 => 4
110010111 => 001011111 => 5
110011000 => 000001111 => 4
110011001 => 001001111 => 4
110011010 => 000110111 => 5
110011011 => 001101111 => 5
110011100 => 000011111 => 5
110011101 => 001110111 => 7
110011110 => 000111111 => 6
110011111 => 001111111 => 7
110100000 => 000000111 => 3
110100001 => 000010111 => 3
110100010 => 000010111 => 3
110100011 => 000110111 => 5
110100100 => 000010111 => 3
110100101 => 001010111 => 5
110100110 => 000110111 => 5
110100111 => 001110111 => 7
110101000 => 000010111 => 3
110101001 => 001010111 => 5
110101010 => 001010111 => 5
110101011 => 010101111 => 5
110101100 => 000101111 => 4
110101101 => 010101111 => 5
110101110 => 001011111 => 5
110101111 => 010111111 => 6
110110000 => 000001111 => 4
110110001 => 000101111 => 4
110110010 => 000101111 => 4
110110011 => 001101111 => 5
110110100 => 000101111 => 4
110110101 => 010101111 => 5
110110110 => 001101111 => 5
110110111 => 011011111 => 5
110111000 => 000011111 => 5
110111001 => 001011111 => 5
110111010 => 001011111 => 5
110111011 => 011011111 => 5
110111100 => 000111111 => 6
110111101 => 010111111 => 6
110111110 => 001111111 => 7
110111111 => 011111111 => 8
111000000 => 000000111 => 3
111000001 => 000001111 => 4
111000010 => 000001111 => 4
111000011 => 000011111 => 5
111000100 => 000001111 => 4
111000101 => 000101111 => 4
111000110 => 000011111 => 5
111000111 => 000111111 => 6
111001000 => 000001111 => 4
111001001 => 001001111 => 4
111001010 => 000101111 => 4
111001011 => 001011111 => 5
111001100 => 000011111 => 5
111001101 => 001101111 => 5
111001110 => 000111111 => 6
111001111 => 001111111 => 7
111010000 => 000001111 => 4
111010001 => 000101111 => 4
111010010 => 000101111 => 4
111010011 => 001101111 => 5
111010100 => 000101111 => 4
111010101 => 010101111 => 5
111010110 => 001011111 => 5
111010111 => 010111111 => 6
111011000 => 000011111 => 5
111011001 => 001011111 => 5
111011010 => 001011111 => 5
111011011 => 011011111 => 5
111011100 => 000111111 => 6
111011101 => 010111111 => 6
111011110 => 001111111 => 7
111011111 => 011111111 => 8
111100000 => 000001111 => 4
111100001 => 000011111 => 5
111100010 => 000011111 => 5
111100011 => 000111111 => 6
111100100 => 000011111 => 5
111100101 => 001011111 => 5
111100110 => 000111111 => 6
111100111 => 001111111 => 7
111101000 => 000011111 => 5
111101001 => 001011111 => 5
111101010 => 001011111 => 5
111101011 => 010111111 => 6
111101100 => 000111111 => 6
111101101 => 010111111 => 6
111101110 => 001111111 => 7
111101111 => 011111111 => 8
111110000 => 000011111 => 5
111110001 => 000111111 => 6
111110010 => 000111111 => 6
111110011 => 001111111 => 7
111110100 => 000111111 => 6
111110101 => 010111111 => 6
111110110 => 001111111 => 7
111110111 => 011111111 => 8
111111000 => 000111111 => 6
111111001 => 001111111 => 7
111111010 => 001111111 => 7
111111011 => 011111111 => 8
111111100 => 001111111 => 7
111111101 => 011111111 => 8
111111110 => 011111111 => 8
111111111 => 111111111 => 9
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,1 1,3,3,1 1,4,5,5,1 1,5,7,13,5,1 1,6,9,29,10,8,1 1,7,11,48,26,27,7,1 1,8,13,67,56,83,17,10,1 1,9,15,86,111,181,53,45,10,1
$F_{1} = 1 + q$
$F_{2} = 1 + 2\ q + q^{2}$
$F_{3} = 1 + 3\ q + 3\ q^{2} + q^{3}$
$F_{4} = 1 + 4\ q + 5\ q^{2} + 5\ q^{3} + q^{4}$
$F_{5} = 1 + 5\ q + 7\ q^{2} + 13\ q^{3} + 5\ q^{4} + q^{5}$
$F_{6} = 1 + 6\ q + 9\ q^{2} + 29\ q^{3} + 10\ q^{4} + 8\ q^{5} + q^{6}$
$F_{7} = 1 + 7\ q + 11\ q^{2} + 48\ q^{3} + 26\ q^{4} + 27\ q^{5} + 7\ q^{6} + q^{7}$
$F_{8} = 1 + 8\ q + 13\ q^{2} + 67\ q^{3} + 56\ q^{4} + 83\ q^{5} + 17\ q^{6} + 10\ q^{7} + q^{8}$
$F_{9} = 1 + 9\ q + 15\ q^{2} + 86\ q^{3} + 111\ q^{4} + 181\ q^{5} + 53\ q^{6} + 45\ q^{7} + 10\ q^{8} + q^{9}$
Description
The length of the longest palindromic factor beginning with a one of a binary word.
Map
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.
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