Identifier
-
Mp00234:
Binary words
—valleys-to-peaks⟶
Binary words
St001419: Binary words ⟶ ℤ
Values
0 => 1 => 1
1 => 1 => 1
00 => 01 => 1
01 => 10 => 1
10 => 11 => 2
11 => 11 => 2
000 => 001 => 1
001 => 010 => 1
010 => 101 => 3
011 => 101 => 3
100 => 101 => 3
101 => 110 => 2
110 => 111 => 3
111 => 111 => 3
0000 => 0001 => 1
0001 => 0010 => 1
0010 => 0101 => 3
0011 => 0101 => 3
0100 => 1001 => 4
0101 => 1010 => 3
0110 => 1011 => 3
0111 => 1011 => 3
1000 => 1001 => 4
1001 => 1010 => 3
1010 => 1101 => 3
1011 => 1101 => 3
1100 => 1101 => 3
1101 => 1110 => 3
1110 => 1111 => 4
1111 => 1111 => 4
00000 => 00001 => 1
00001 => 00010 => 1
00010 => 00101 => 3
00011 => 00101 => 3
00100 => 01001 => 4
00101 => 01010 => 3
00110 => 01011 => 3
00111 => 01011 => 3
01000 => 10001 => 5
01001 => 10010 => 4
01010 => 10101 => 5
01011 => 10101 => 5
01100 => 10101 => 5
01101 => 10110 => 3
01110 => 10111 => 3
01111 => 10111 => 3
10000 => 10001 => 5
10001 => 10010 => 4
10010 => 10101 => 5
10011 => 10101 => 5
10100 => 11001 => 4
10101 => 11010 => 3
10110 => 11011 => 5
10111 => 11011 => 5
11000 => 11001 => 4
11001 => 11010 => 3
11010 => 11101 => 3
11011 => 11101 => 3
11100 => 11101 => 3
11101 => 11110 => 4
11110 => 11111 => 5
11111 => 11111 => 5
000000 => 000001 => 1
000001 => 000010 => 1
000010 => 000101 => 3
000011 => 000101 => 3
000100 => 001001 => 4
000101 => 001010 => 3
000110 => 001011 => 3
000111 => 001011 => 3
001000 => 010001 => 5
001001 => 010010 => 4
001010 => 010101 => 5
001011 => 010101 => 5
001100 => 010101 => 5
001101 => 010110 => 3
001110 => 010111 => 3
001111 => 010111 => 3
010000 => 100001 => 6
010001 => 100010 => 5
010010 => 100101 => 4
010011 => 100101 => 4
010100 => 101001 => 4
010101 => 101010 => 5
010110 => 101011 => 5
010111 => 101011 => 5
011000 => 101001 => 4
011001 => 101010 => 5
011010 => 101101 => 6
011011 => 101101 => 6
011100 => 101101 => 6
011101 => 101110 => 3
011110 => 101111 => 4
011111 => 101111 => 4
100000 => 100001 => 6
100001 => 100010 => 5
100010 => 100101 => 4
100011 => 100101 => 4
100100 => 101001 => 4
100101 => 101010 => 5
100110 => 101011 => 5
>>> Load all 1022 entries. <<<100111 => 101011 => 5
101000 => 110001 => 5
101001 => 110010 => 4
101010 => 110101 => 5
101011 => 110101 => 5
101100 => 110101 => 5
101101 => 110110 => 5
101110 => 110111 => 5
101111 => 110111 => 5
110000 => 110001 => 5
110001 => 110010 => 4
110010 => 110101 => 5
110011 => 110101 => 5
110100 => 111001 => 4
110101 => 111010 => 3
110110 => 111011 => 5
110111 => 111011 => 5
111000 => 111001 => 4
111001 => 111010 => 3
111010 => 111101 => 4
111011 => 111101 => 4
111100 => 111101 => 4
111101 => 111110 => 5
111110 => 111111 => 6
111111 => 111111 => 6
0000000 => 0000001 => 1
0000001 => 0000010 => 1
0000010 => 0000101 => 3
0000011 => 0000101 => 3
0000100 => 0001001 => 4
0000101 => 0001010 => 3
0000110 => 0001011 => 3
0000111 => 0001011 => 3
0001000 => 0010001 => 5
0001001 => 0010010 => 4
0001010 => 0010101 => 5
0001011 => 0010101 => 5
0001100 => 0010101 => 5
0001101 => 0010110 => 3
0001110 => 0010111 => 3
0001111 => 0010111 => 3
0010000 => 0100001 => 6
0010001 => 0100010 => 5
0010010 => 0100101 => 4
0010011 => 0100101 => 4
0010100 => 0101001 => 4
0010101 => 0101010 => 5
0010110 => 0101011 => 5
0010111 => 0101011 => 5
0011000 => 0101001 => 4
0011001 => 0101010 => 5
0011010 => 0101101 => 6
0011011 => 0101101 => 6
0011100 => 0101101 => 6
0011101 => 0101110 => 3
0011110 => 0101111 => 4
0011111 => 0101111 => 4
0100000 => 1000001 => 7
0100001 => 1000010 => 6
0100010 => 1000101 => 5
0100011 => 1000101 => 5
0100100 => 1001001 => 7
0100101 => 1001010 => 4
0100110 => 1001011 => 4
0100111 => 1001011 => 4
0101000 => 1010001 => 5
0101001 => 1010010 => 4
0101010 => 1010101 => 7
0101011 => 1010101 => 7
0101100 => 1010101 => 7
0101101 => 1010110 => 5
0101110 => 1010111 => 5
0101111 => 1010111 => 5
0110000 => 1010001 => 5
0110001 => 1010010 => 4
0110010 => 1010101 => 7
0110011 => 1010101 => 7
0110100 => 1011001 => 4
0110101 => 1011010 => 6
0110110 => 1011011 => 6
0110111 => 1011011 => 6
0111000 => 1011001 => 4
0111001 => 1011010 => 6
0111010 => 1011101 => 7
0111011 => 1011101 => 7
0111100 => 1011101 => 7
0111101 => 1011110 => 4
0111110 => 1011111 => 5
0111111 => 1011111 => 5
1000000 => 1000001 => 7
1000001 => 1000010 => 6
1000010 => 1000101 => 5
1000011 => 1000101 => 5
1000100 => 1001001 => 7
1000101 => 1001010 => 4
1000110 => 1001011 => 4
1000111 => 1001011 => 4
1001000 => 1010001 => 5
1001001 => 1010010 => 4
1001010 => 1010101 => 7
1001011 => 1010101 => 7
1001100 => 1010101 => 7
1001101 => 1010110 => 5
1001110 => 1010111 => 5
1001111 => 1010111 => 5
1010000 => 1100001 => 6
1010001 => 1100010 => 5
1010010 => 1100101 => 4
1010011 => 1100101 => 4
1010100 => 1101001 => 4
1010101 => 1101010 => 5
1010110 => 1101011 => 7
1010111 => 1101011 => 7
1011000 => 1101001 => 4
1011001 => 1101010 => 5
1011010 => 1101101 => 6
1011011 => 1101101 => 6
1011100 => 1101101 => 6
1011101 => 1101110 => 5
1011110 => 1101111 => 5
1011111 => 1101111 => 5
1100000 => 1100001 => 6
1100001 => 1100010 => 5
1100010 => 1100101 => 4
1100011 => 1100101 => 4
1100100 => 1101001 => 4
1100101 => 1101010 => 5
1100110 => 1101011 => 7
1100111 => 1101011 => 7
1101000 => 1110001 => 5
1101001 => 1110010 => 4
1101010 => 1110101 => 5
1101011 => 1110101 => 5
1101100 => 1110101 => 5
1101101 => 1110110 => 5
1101110 => 1110111 => 7
1101111 => 1110111 => 7
1110000 => 1110001 => 5
1110001 => 1110010 => 4
1110010 => 1110101 => 5
1110011 => 1110101 => 5
1110100 => 1111001 => 4
1110101 => 1111010 => 4
1110110 => 1111011 => 5
1110111 => 1111011 => 5
1111000 => 1111001 => 4
1111001 => 1111010 => 4
1111010 => 1111101 => 5
1111011 => 1111101 => 5
1111100 => 1111101 => 5
1111101 => 1111110 => 6
1111110 => 1111111 => 7
1111111 => 1111111 => 7
00000000 => 00000001 => 1
00000001 => 00000010 => 1
00000010 => 00000101 => 3
00000011 => 00000101 => 3
00000100 => 00001001 => 4
00000101 => 00001010 => 3
00000110 => 00001011 => 3
00000111 => 00001011 => 3
00001000 => 00010001 => 5
00001001 => 00010010 => 4
00001010 => 00010101 => 5
00001011 => 00010101 => 5
00001100 => 00010101 => 5
00001101 => 00010110 => 3
00001110 => 00010111 => 3
00001111 => 00010111 => 3
00010000 => 00100001 => 6
00010001 => 00100010 => 5
00010010 => 00100101 => 4
00010011 => 00100101 => 4
00010100 => 00101001 => 4
00010101 => 00101010 => 5
00010110 => 00101011 => 5
00010111 => 00101011 => 5
00011000 => 00101001 => 4
00011001 => 00101010 => 5
00011010 => 00101101 => 6
00011011 => 00101101 => 6
00011100 => 00101101 => 6
00011101 => 00101110 => 3
00011110 => 00101111 => 4
00011111 => 00101111 => 4
00100000 => 01000001 => 7
00100001 => 01000010 => 6
00100010 => 01000101 => 5
00100011 => 01000101 => 5
00100100 => 01001001 => 7
00100101 => 01001010 => 4
00100110 => 01001011 => 4
00100111 => 01001011 => 4
00101000 => 01010001 => 5
00101001 => 01010010 => 4
00101010 => 01010101 => 7
00101011 => 01010101 => 7
00101100 => 01010101 => 7
00101101 => 01010110 => 5
00101110 => 01010111 => 5
00101111 => 01010111 => 5
00110000 => 01010001 => 5
00110001 => 01010010 => 4
00110010 => 01010101 => 7
00110011 => 01010101 => 7
00110100 => 01011001 => 4
00110101 => 01011010 => 6
00110110 => 01011011 => 6
00110111 => 01011011 => 6
00111000 => 01011001 => 4
00111001 => 01011010 => 6
00111010 => 01011101 => 7
00111011 => 01011101 => 7
00111100 => 01011101 => 7
00111101 => 01011110 => 4
00111110 => 01011111 => 5
00111111 => 01011111 => 5
01000000 => 10000001 => 8
01000001 => 10000010 => 7
01000010 => 10000101 => 6
01000011 => 10000101 => 6
01000100 => 10001001 => 5
01000101 => 10001010 => 5
01000110 => 10001011 => 5
01000111 => 10001011 => 5
01001000 => 10010001 => 5
01001001 => 10010010 => 7
01001010 => 10010101 => 5
01001011 => 10010101 => 5
01001100 => 10010101 => 5
01001101 => 10010110 => 4
01001110 => 10010111 => 4
01001111 => 10010111 => 4
01010000 => 10100001 => 6
01010001 => 10100010 => 5
01010010 => 10100101 => 8
01010011 => 10100101 => 8
01010100 => 10101001 => 5
01010101 => 10101010 => 7
01010110 => 10101011 => 7
01010111 => 10101011 => 7
01011000 => 10101001 => 5
01011001 => 10101010 => 7
01011010 => 10101101 => 6
01011011 => 10101101 => 6
01011100 => 10101101 => 6
01011101 => 10101110 => 5
01011110 => 10101111 => 5
01011111 => 10101111 => 5
01100000 => 10100001 => 6
01100001 => 10100010 => 5
01100010 => 10100101 => 8
01100011 => 10100101 => 8
01100100 => 10101001 => 5
01100101 => 10101010 => 7
01100110 => 10101011 => 7
01100111 => 10101011 => 7
01101000 => 10110001 => 5
01101001 => 10110010 => 4
01101010 => 10110101 => 6
01101011 => 10110101 => 6
01101100 => 10110101 => 6
01101101 => 10110110 => 6
01101110 => 10110111 => 6
01101111 => 10110111 => 6
01110000 => 10110001 => 5
01110001 => 10110010 => 4
01110010 => 10110101 => 6
01110011 => 10110101 => 6
01110100 => 10111001 => 4
01110101 => 10111010 => 7
01110110 => 10111011 => 7
01110111 => 10111011 => 7
01111000 => 10111001 => 4
01111001 => 10111010 => 7
01111010 => 10111101 => 8
01111011 => 10111101 => 8
01111100 => 10111101 => 8
01111101 => 10111110 => 5
01111110 => 10111111 => 6
01111111 => 10111111 => 6
10000000 => 10000001 => 8
10000001 => 10000010 => 7
10000010 => 10000101 => 6
10000011 => 10000101 => 6
10000100 => 10001001 => 5
10000101 => 10001010 => 5
10000110 => 10001011 => 5
10000111 => 10001011 => 5
10001000 => 10010001 => 5
10001001 => 10010010 => 7
10001010 => 10010101 => 5
10001011 => 10010101 => 5
10001100 => 10010101 => 5
10001101 => 10010110 => 4
10001110 => 10010111 => 4
10001111 => 10010111 => 4
10010000 => 10100001 => 6
10010001 => 10100010 => 5
10010010 => 10100101 => 8
10010011 => 10100101 => 8
10010100 => 10101001 => 5
10010101 => 10101010 => 7
10010110 => 10101011 => 7
10010111 => 10101011 => 7
10011000 => 10101001 => 5
10011001 => 10101010 => 7
10011010 => 10101101 => 6
10011011 => 10101101 => 6
10011100 => 10101101 => 6
10011101 => 10101110 => 5
10011110 => 10101111 => 5
10011111 => 10101111 => 5
10100000 => 11000001 => 7
10100001 => 11000010 => 6
10100010 => 11000101 => 5
10100011 => 11000101 => 5
10100100 => 11001001 => 7
10100101 => 11001010 => 4
10100110 => 11001011 => 4
10100111 => 11001011 => 4
10101000 => 11010001 => 5
10101001 => 11010010 => 4
10101010 => 11010101 => 7
10101011 => 11010101 => 7
10101100 => 11010101 => 7
10101101 => 11010110 => 7
10101110 => 11010111 => 7
10101111 => 11010111 => 7
10110000 => 11010001 => 5
10110001 => 11010010 => 4
10110010 => 11010101 => 7
10110011 => 11010101 => 7
10110100 => 11011001 => 5
10110101 => 11011010 => 6
10110110 => 11011011 => 8
10110111 => 11011011 => 8
10111000 => 11011001 => 5
10111001 => 11011010 => 6
10111010 => 11011101 => 7
10111011 => 11011101 => 7
10111100 => 11011101 => 7
10111101 => 11011110 => 5
10111110 => 11011111 => 5
10111111 => 11011111 => 5
11000000 => 11000001 => 7
11000001 => 11000010 => 6
11000010 => 11000101 => 5
11000011 => 11000101 => 5
11000100 => 11001001 => 7
11000101 => 11001010 => 4
11000110 => 11001011 => 4
11000111 => 11001011 => 4
11001000 => 11010001 => 5
11001001 => 11010010 => 4
11001010 => 11010101 => 7
11001011 => 11010101 => 7
11001100 => 11010101 => 7
11001101 => 11010110 => 7
11001110 => 11010111 => 7
11001111 => 11010111 => 7
11010000 => 11100001 => 6
11010001 => 11100010 => 5
11010010 => 11100101 => 4
11010011 => 11100101 => 4
11010100 => 11101001 => 4
11010101 => 11101010 => 5
11010110 => 11101011 => 7
11010111 => 11101011 => 7
11011000 => 11101001 => 4
11011001 => 11101010 => 5
11011010 => 11101101 => 6
11011011 => 11101101 => 6
11011100 => 11101101 => 6
11011101 => 11101110 => 7
11011110 => 11101111 => 7
11011111 => 11101111 => 7
11100000 => 11100001 => 6
11100001 => 11100010 => 5
11100010 => 11100101 => 4
11100011 => 11100101 => 4
11100100 => 11101001 => 4
11100101 => 11101010 => 5
11100110 => 11101011 => 7
11100111 => 11101011 => 7
11101000 => 11110001 => 5
11101001 => 11110010 => 4
11101010 => 11110101 => 5
11101011 => 11110101 => 5
11101100 => 11110101 => 5
11101101 => 11110110 => 5
11101110 => 11110111 => 7
11101111 => 11110111 => 7
11110000 => 11110001 => 5
11110001 => 11110010 => 4
11110010 => 11110101 => 5
11110011 => 11110101 => 5
11110100 => 11111001 => 5
11110101 => 11111010 => 5
11110110 => 11111011 => 5
11110111 => 11111011 => 5
11111000 => 11111001 => 5
11111001 => 11111010 => 5
11111010 => 11111101 => 6
11111011 => 11111101 => 6
11111100 => 11111101 => 6
11111101 => 11111110 => 7
11111110 => 11111111 => 8
11111111 => 11111111 => 8
000000000 => 000000001 => 1
000000001 => 000000010 => 1
000000010 => 000000101 => 3
000000011 => 000000101 => 3
000000100 => 000001001 => 4
000000101 => 000001010 => 3
000000110 => 000001011 => 3
000000111 => 000001011 => 3
000001000 => 000010001 => 5
000001001 => 000010010 => 4
000001010 => 000010101 => 5
000001011 => 000010101 => 5
000001100 => 000010101 => 5
000001101 => 000010110 => 3
000001110 => 000010111 => 3
000001111 => 000010111 => 3
000010000 => 000100001 => 6
000010001 => 000100010 => 5
000010010 => 000100101 => 4
000010011 => 000100101 => 4
000010100 => 000101001 => 4
000010101 => 000101010 => 5
000010110 => 000101011 => 5
000010111 => 000101011 => 5
000011000 => 000101001 => 4
000011001 => 000101010 => 5
000011010 => 000101101 => 6
000011011 => 000101101 => 6
000011100 => 000101101 => 6
000011101 => 000101110 => 3
000011110 => 000101111 => 4
000011111 => 000101111 => 4
000100000 => 001000001 => 7
000100001 => 001000010 => 6
000100010 => 001000101 => 5
000100011 => 001000101 => 5
000100100 => 001001001 => 7
000100101 => 001001010 => 4
000100110 => 001001011 => 4
000100111 => 001001011 => 4
000101000 => 001010001 => 5
000101001 => 001010010 => 4
000101010 => 001010101 => 7
000101011 => 001010101 => 7
000101100 => 001010101 => 7
000101101 => 001010110 => 5
000101110 => 001010111 => 5
000101111 => 001010111 => 5
000110000 => 001010001 => 5
000110001 => 001010010 => 4
000110010 => 001010101 => 7
000110011 => 001010101 => 7
000110100 => 001011001 => 4
000110101 => 001011010 => 6
000110110 => 001011011 => 6
000110111 => 001011011 => 6
000111000 => 001011001 => 4
000111001 => 001011010 => 6
000111010 => 001011101 => 7
000111011 => 001011101 => 7
000111100 => 001011101 => 7
000111101 => 001011110 => 4
000111110 => 001011111 => 5
000111111 => 001011111 => 5
001000000 => 010000001 => 8
001000001 => 010000010 => 7
001000010 => 010000101 => 6
001000011 => 010000101 => 6
001000100 => 010001001 => 5
001000101 => 010001010 => 5
001000110 => 010001011 => 5
001000111 => 010001011 => 5
001001000 => 010010001 => 5
001001001 => 010010010 => 7
001001010 => 010010101 => 5
001001011 => 010010101 => 5
001001100 => 010010101 => 5
001001101 => 010010110 => 4
001001110 => 010010111 => 4
001001111 => 010010111 => 4
001010000 => 010100001 => 6
001010001 => 010100010 => 5
001010010 => 010100101 => 8
001010011 => 010100101 => 8
001010100 => 010101001 => 5
001010101 => 010101010 => 7
001010110 => 010101011 => 7
001010111 => 010101011 => 7
001011000 => 010101001 => 5
001011001 => 010101010 => 7
001011010 => 010101101 => 6
001011011 => 010101101 => 6
001011100 => 010101101 => 6
001011101 => 010101110 => 5
001011110 => 010101111 => 5
001011111 => 010101111 => 5
001100000 => 010100001 => 6
001100001 => 010100010 => 5
001100010 => 010100101 => 8
001100011 => 010100101 => 8
001100100 => 010101001 => 5
001100101 => 010101010 => 7
001100110 => 010101011 => 7
001100111 => 010101011 => 7
001101000 => 010110001 => 5
001101001 => 010110010 => 4
001101010 => 010110101 => 6
001101011 => 010110101 => 6
001101100 => 010110101 => 6
001101101 => 010110110 => 6
001101110 => 010110111 => 6
001101111 => 010110111 => 6
001110000 => 010110001 => 5
001110001 => 010110010 => 4
001110010 => 010110101 => 6
001110011 => 010110101 => 6
001110100 => 010111001 => 4
001110101 => 010111010 => 7
001110110 => 010111011 => 7
001110111 => 010111011 => 7
001111000 => 010111001 => 4
001111001 => 010111010 => 7
001111010 => 010111101 => 8
001111011 => 010111101 => 8
001111100 => 010111101 => 8
001111101 => 010111110 => 5
001111110 => 010111111 => 6
001111111 => 010111111 => 6
010000000 => 100000001 => 9
010000001 => 100000010 => 8
010000010 => 100000101 => 7
010000011 => 100000101 => 7
010000100 => 100001001 => 6
010000101 => 100001010 => 6
010000110 => 100001011 => 6
010000111 => 100001011 => 6
010001000 => 100010001 => 9
010001001 => 100010010 => 5
010001010 => 100010101 => 5
010001011 => 100010101 => 5
010001100 => 100010101 => 5
010001101 => 100010110 => 5
010001110 => 100010111 => 5
010001111 => 100010111 => 5
010010000 => 100100001 => 6
010010001 => 100100010 => 5
010010010 => 100100101 => 7
010010011 => 100100101 => 7
010010100 => 100101001 => 9
010010101 => 100101010 => 5
010010110 => 100101011 => 5
010010111 => 100101011 => 5
010011000 => 100101001 => 9
010011001 => 100101010 => 5
010011010 => 100101101 => 6
010011011 => 100101101 => 6
010011100 => 100101101 => 6
010011101 => 100101110 => 4
010011110 => 100101111 => 4
010011111 => 100101111 => 4
010100000 => 101000001 => 7
010100001 => 101000010 => 6
010100010 => 101000101 => 9
010100011 => 101000101 => 9
010100100 => 101001001 => 7
010100101 => 101001010 => 8
010100110 => 101001011 => 8
010100111 => 101001011 => 8
010101000 => 101010001 => 5
010101001 => 101010010 => 5
010101010 => 101010101 => 9
010101011 => 101010101 => 9
010101100 => 101010101 => 9
010101101 => 101010110 => 7
010101110 => 101010111 => 7
010101111 => 101010111 => 7
010110000 => 101010001 => 5
010110001 => 101010010 => 5
010110010 => 101010101 => 9
010110011 => 101010101 => 9
010110100 => 101011001 => 5
010110101 => 101011010 => 6
010110110 => 101011011 => 6
010110111 => 101011011 => 6
010111000 => 101011001 => 5
010111001 => 101011010 => 6
010111010 => 101011101 => 7
010111011 => 101011101 => 7
010111100 => 101011101 => 7
010111101 => 101011110 => 5
010111110 => 101011111 => 5
010111111 => 101011111 => 5
011000000 => 101000001 => 7
011000001 => 101000010 => 6
011000010 => 101000101 => 9
011000011 => 101000101 => 9
011000100 => 101001001 => 7
011000101 => 101001010 => 8
011000110 => 101001011 => 8
011000111 => 101001011 => 8
011001000 => 101010001 => 5
011001001 => 101010010 => 5
011001010 => 101010101 => 9
011001011 => 101010101 => 9
011001100 => 101010101 => 9
011001101 => 101010110 => 7
011001110 => 101010111 => 7
011001111 => 101010111 => 7
011010000 => 101100001 => 6
011010001 => 101100010 => 5
011010010 => 101100101 => 4
011010011 => 101100101 => 4
011010100 => 101101001 => 6
011010101 => 101101010 => 6
011010110 => 101101011 => 7
011010111 => 101101011 => 7
011011000 => 101101001 => 6
011011001 => 101101010 => 6
011011010 => 101101101 => 9
011011011 => 101101101 => 9
011011100 => 101101101 => 9
011011101 => 101101110 => 6
011011110 => 101101111 => 6
011011111 => 101101111 => 6
011100000 => 101100001 => 6
011100001 => 101100010 => 5
011100010 => 101100101 => 4
011100011 => 101100101 => 4
011100100 => 101101001 => 6
011100101 => 101101010 => 6
011100110 => 101101011 => 7
011100111 => 101101011 => 7
011101000 => 101110001 => 5
011101001 => 101110010 => 4
011101010 => 101110101 => 7
011101011 => 101110101 => 7
011101100 => 101110101 => 7
011101101 => 101110110 => 7
011101110 => 101110111 => 7
011101111 => 101110111 => 7
011110000 => 101110001 => 5
011110001 => 101110010 => 4
011110010 => 101110101 => 7
011110011 => 101110101 => 7
011110100 => 101111001 => 4
011110101 => 101111010 => 8
011110110 => 101111011 => 8
011110111 => 101111011 => 8
011111000 => 101111001 => 4
011111001 => 101111010 => 8
011111010 => 101111101 => 9
011111011 => 101111101 => 9
011111100 => 101111101 => 9
011111101 => 101111110 => 6
011111110 => 101111111 => 7
011111111 => 101111111 => 7
100000000 => 100000001 => 9
100000001 => 100000010 => 8
100000010 => 100000101 => 7
100000011 => 100000101 => 7
100000100 => 100001001 => 6
100000101 => 100001010 => 6
100000110 => 100001011 => 6
100000111 => 100001011 => 6
100001000 => 100010001 => 9
100001001 => 100010010 => 5
100001010 => 100010101 => 5
100001011 => 100010101 => 5
100001100 => 100010101 => 5
100001101 => 100010110 => 5
100001110 => 100010111 => 5
100001111 => 100010111 => 5
100010000 => 100100001 => 6
100010001 => 100100010 => 5
100010010 => 100100101 => 7
100010011 => 100100101 => 7
100010100 => 100101001 => 9
100010101 => 100101010 => 5
100010110 => 100101011 => 5
100010111 => 100101011 => 5
100011000 => 100101001 => 9
100011001 => 100101010 => 5
100011010 => 100101101 => 6
100011011 => 100101101 => 6
100011100 => 100101101 => 6
100011101 => 100101110 => 4
100011110 => 100101111 => 4
100011111 => 100101111 => 4
100100000 => 101000001 => 7
100100001 => 101000010 => 6
100100010 => 101000101 => 9
100100011 => 101000101 => 9
100100100 => 101001001 => 7
100100101 => 101001010 => 8
100100110 => 101001011 => 8
100100111 => 101001011 => 8
100101000 => 101010001 => 5
100101001 => 101010010 => 5
100101010 => 101010101 => 9
100101011 => 101010101 => 9
100101100 => 101010101 => 9
100101101 => 101010110 => 7
100101110 => 101010111 => 7
100101111 => 101010111 => 7
100110000 => 101010001 => 5
100110001 => 101010010 => 5
100110010 => 101010101 => 9
100110011 => 101010101 => 9
100110100 => 101011001 => 5
100110101 => 101011010 => 6
100110110 => 101011011 => 6
100110111 => 101011011 => 6
100111000 => 101011001 => 5
100111001 => 101011010 => 6
100111010 => 101011101 => 7
100111011 => 101011101 => 7
100111100 => 101011101 => 7
100111101 => 101011110 => 5
100111110 => 101011111 => 5
100111111 => 101011111 => 5
101000000 => 110000001 => 8
101000001 => 110000010 => 7
101000010 => 110000101 => 6
101000011 => 110000101 => 6
101000100 => 110001001 => 5
101000101 => 110001010 => 5
101000110 => 110001011 => 5
101000111 => 110001011 => 5
101001000 => 110010001 => 5
101001001 => 110010010 => 7
101001010 => 110010101 => 5
101001011 => 110010101 => 5
101001100 => 110010101 => 5
101001101 => 110010110 => 4
101001110 => 110010111 => 4
101001111 => 110010111 => 4
101010000 => 110100001 => 6
101010001 => 110100010 => 5
101010010 => 110100101 => 8
101010011 => 110100101 => 8
101010100 => 110101001 => 5
101010101 => 110101010 => 7
101010110 => 110101011 => 9
101010111 => 110101011 => 9
101011000 => 110101001 => 5
101011001 => 110101010 => 7
101011010 => 110101101 => 7
101011011 => 110101101 => 7
101011100 => 110101101 => 7
101011101 => 110101110 => 7
101011110 => 110101111 => 7
101011111 => 110101111 => 7
101100000 => 110100001 => 6
101100001 => 110100010 => 5
101100010 => 110100101 => 8
101100011 => 110100101 => 8
101100100 => 110101001 => 5
101100101 => 110101010 => 7
101100110 => 110101011 => 9
101100111 => 110101011 => 9
101101000 => 110110001 => 5
101101001 => 110110010 => 5
101101010 => 110110101 => 6
101101011 => 110110101 => 6
101101100 => 110110101 => 6
101101101 => 110110110 => 8
101101110 => 110110111 => 8
101101111 => 110110111 => 8
101110000 => 110110001 => 5
101110001 => 110110010 => 5
101110010 => 110110101 => 6
101110011 => 110110101 => 6
101110100 => 110111001 => 5
101110101 => 110111010 => 7
101110110 => 110111011 => 9
101110111 => 110111011 => 9
101111000 => 110111001 => 5
101111001 => 110111010 => 7
101111010 => 110111101 => 8
101111011 => 110111101 => 8
101111100 => 110111101 => 8
101111101 => 110111110 => 5
101111110 => 110111111 => 6
101111111 => 110111111 => 6
110000000 => 110000001 => 8
110000001 => 110000010 => 7
110000010 => 110000101 => 6
110000011 => 110000101 => 6
110000100 => 110001001 => 5
110000101 => 110001010 => 5
110000110 => 110001011 => 5
110000111 => 110001011 => 5
110001000 => 110010001 => 5
110001001 => 110010010 => 7
110001010 => 110010101 => 5
110001011 => 110010101 => 5
110001100 => 110010101 => 5
110001101 => 110010110 => 4
110001110 => 110010111 => 4
110001111 => 110010111 => 4
110010000 => 110100001 => 6
110010001 => 110100010 => 5
110010010 => 110100101 => 8
110010011 => 110100101 => 8
110010100 => 110101001 => 5
110010101 => 110101010 => 7
110010110 => 110101011 => 9
110010111 => 110101011 => 9
110011000 => 110101001 => 5
110011001 => 110101010 => 7
110011010 => 110101101 => 7
110011011 => 110101101 => 7
110011100 => 110101101 => 7
110011101 => 110101110 => 7
110011110 => 110101111 => 7
110011111 => 110101111 => 7
110100000 => 111000001 => 7
110100001 => 111000010 => 6
110100010 => 111000101 => 5
110100011 => 111000101 => 5
110100100 => 111001001 => 7
110100101 => 111001010 => 4
110100110 => 111001011 => 4
110100111 => 111001011 => 4
110101000 => 111010001 => 5
110101001 => 111010010 => 4
110101010 => 111010101 => 7
110101011 => 111010101 => 7
110101100 => 111010101 => 7
110101101 => 111010110 => 7
110101110 => 111010111 => 9
110101111 => 111010111 => 9
110110000 => 111010001 => 5
110110001 => 111010010 => 4
110110010 => 111010101 => 7
110110011 => 111010101 => 7
110110100 => 111011001 => 5
110110101 => 111011010 => 6
110110110 => 111011011 => 8
110110111 => 111011011 => 8
110111000 => 111011001 => 5
110111001 => 111011010 => 6
110111010 => 111011101 => 7
110111011 => 111011101 => 7
110111100 => 111011101 => 7
110111101 => 111011110 => 7
110111110 => 111011111 => 7
110111111 => 111011111 => 7
111000000 => 111000001 => 7
111000001 => 111000010 => 6
111000010 => 111000101 => 5
111000011 => 111000101 => 5
111000100 => 111001001 => 7
111000101 => 111001010 => 4
111000110 => 111001011 => 4
111000111 => 111001011 => 4
111001000 => 111010001 => 5
111001001 => 111010010 => 4
111001010 => 111010101 => 7
111001011 => 111010101 => 7
111001100 => 111010101 => 7
111001101 => 111010110 => 7
111001110 => 111010111 => 9
111001111 => 111010111 => 9
111010000 => 111100001 => 6
111010001 => 111100010 => 5
111010010 => 111100101 => 4
111010011 => 111100101 => 4
111010100 => 111101001 => 4
111010101 => 111101010 => 5
111010110 => 111101011 => 7
111010111 => 111101011 => 7
111011000 => 111101001 => 4
111011001 => 111101010 => 5
111011010 => 111101101 => 6
111011011 => 111101101 => 6
111011100 => 111101101 => 6
111011101 => 111101110 => 7
111011110 => 111101111 => 9
111011111 => 111101111 => 9
111100000 => 111100001 => 6
111100001 => 111100010 => 5
111100010 => 111100101 => 4
111100011 => 111100101 => 4
111100100 => 111101001 => 4
111100101 => 111101010 => 5
111100110 => 111101011 => 7
111100111 => 111101011 => 7
111101000 => 111110001 => 5
111101001 => 111110010 => 5
111101010 => 111110101 => 5
111101011 => 111110101 => 5
111101100 => 111110101 => 5
111101101 => 111110110 => 5
111101110 => 111110111 => 7
111101111 => 111110111 => 7
111110000 => 111110001 => 5
111110001 => 111110010 => 5
111110010 => 111110101 => 5
111110011 => 111110101 => 5
111110100 => 111111001 => 6
111110101 => 111111010 => 6
111110110 => 111111011 => 6
111110111 => 111111011 => 6
111111000 => 111111001 => 6
111111001 => 111111010 => 6
111111010 => 111111101 => 7
111111011 => 111111101 => 7
111111100 => 111111101 => 7
111111101 => 111111110 => 8
111111110 => 111111111 => 9
111111111 => 111111111 => 9
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Generating function
click to show known generating functions
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,2 2,1,5 2,0,10,4 2,0,13,6,11 2,0,11,18,26,7 2,0,9,33,45,16,23 2,0,9,44,82,44,60,15 2,0,9,59,140,94,119,40,49
F1=2 q
F2=2 q+2 q2
F3=2 q+q2+5 q3
F4=2 q+10 q3+4 q4
F5=2 q+13 q3+6 q4+11 q5
F6=2 q+11 q3+18 q4+26 q5+7 q6
F7=2 q+9 q3+33 q4+45 q5+16 q6+23 q7
F8=2 q+9 q3+44 q4+82 q5+44 q6+60 q7+15 q8
F9=2 q+9 q3+59 q4+140 q5+94 q6+119 q7+40 q8+49 q9
Description
The length of the longest palindromic factor beginning with a one of a binary word.
Map
valleys-to-peaks
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence 01, or a trailing 0. A peak is a subsequence 10 or a trailing 1. This map replaces every valley with a peak.
A valley in a binary word is a subsequence 01, or a trailing 0. A peak is a subsequence 10 or a trailing 1. This map replaces every valley with a peak.
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