Identifier
-
Mp00104:
Binary words
—reverse⟶
Binary words
St000347: Binary words ⟶ ℤ
Values
0 => 0 => 0
1 => 1 => 0
00 => 00 => 0
01 => 10 => 1
10 => 01 => 0
11 => 11 => 0
000 => 000 => 0
001 => 100 => 3
010 => 010 => 1
011 => 110 => 3
100 => 001 => 0
101 => 101 => 1
110 => 011 => 0
111 => 111 => 0
0000 => 0000 => 0
0001 => 1000 => 6
0010 => 0100 => 3
0011 => 1100 => 8
0100 => 0010 => 1
0101 => 1010 => 5
0110 => 0110 => 3
0111 => 1110 => 6
1000 => 0001 => 0
1001 => 1001 => 3
1010 => 0101 => 1
1011 => 1101 => 3
1100 => 0011 => 0
1101 => 1011 => 1
1110 => 0111 => 0
1111 => 1111 => 0
00000 => 00000 => 0
00001 => 10000 => 10
00010 => 01000 => 6
00011 => 11000 => 15
00100 => 00100 => 3
00101 => 10100 => 11
00110 => 01100 => 8
00111 => 11100 => 15
01000 => 00010 => 1
01001 => 10010 => 8
01010 => 01010 => 5
01011 => 11010 => 11
01100 => 00110 => 3
01101 => 10110 => 8
01110 => 01110 => 6
01111 => 11110 => 10
10000 => 00001 => 0
10001 => 10001 => 6
10010 => 01001 => 3
10011 => 11001 => 8
10100 => 00101 => 1
10101 => 10101 => 5
10110 => 01101 => 3
10111 => 11101 => 6
11000 => 00011 => 0
11001 => 10011 => 3
11010 => 01011 => 1
11011 => 11011 => 3
11100 => 00111 => 0
11101 => 10111 => 1
11110 => 01111 => 0
11111 => 11111 => 0
000000 => 000000 => 0
000001 => 100000 => 15
000010 => 010000 => 10
000011 => 110000 => 24
000100 => 001000 => 6
000101 => 101000 => 19
000110 => 011000 => 15
000111 => 111000 => 27
001000 => 000100 => 3
001001 => 100100 => 15
001010 => 010100 => 11
001011 => 110100 => 22
001100 => 001100 => 8
001101 => 101100 => 18
001110 => 011100 => 15
001111 => 111100 => 24
010000 => 000010 => 1
010001 => 100010 => 12
010010 => 010010 => 8
010011 => 110010 => 18
010100 => 001010 => 5
010101 => 101010 => 14
010110 => 011010 => 11
010111 => 111010 => 19
011000 => 000110 => 3
011001 => 100110 => 11
011010 => 010110 => 8
011011 => 110110 => 15
011100 => 001110 => 6
011101 => 101110 => 12
011110 => 011110 => 10
011111 => 111110 => 15
100000 => 000001 => 0
100001 => 100001 => 10
100010 => 010001 => 6
100011 => 110001 => 15
100100 => 001001 => 3
100101 => 101001 => 11
100110 => 011001 => 8
>>> Load all 1191 entries. <<<100111 => 111001 => 15
101000 => 000101 => 1
101001 => 100101 => 8
101010 => 010101 => 5
101011 => 110101 => 11
101100 => 001101 => 3
101101 => 101101 => 8
101110 => 011101 => 6
101111 => 111101 => 10
110000 => 000011 => 0
110001 => 100011 => 6
110010 => 010011 => 3
110011 => 110011 => 8
110100 => 001011 => 1
110101 => 101011 => 5
110110 => 011011 => 3
110111 => 111011 => 6
111000 => 000111 => 0
111001 => 100111 => 3
111010 => 010111 => 1
111011 => 110111 => 3
111100 => 001111 => 0
111101 => 101111 => 1
111110 => 011111 => 0
111111 => 111111 => 0
0000000 => 0000000 => 0
0000001 => 1000000 => 21
0000010 => 0100000 => 15
0000011 => 1100000 => 35
0000100 => 0010000 => 10
0000101 => 1010000 => 29
0000110 => 0110000 => 24
0000111 => 1110000 => 42
0001000 => 0001000 => 6
0001001 => 1001000 => 24
0001010 => 0101000 => 19
0001011 => 1101000 => 36
0001100 => 0011000 => 15
0001101 => 1011000 => 31
0001110 => 0111000 => 27
0001111 => 1111000 => 42
0010000 => 0000100 => 3
0010001 => 1000100 => 20
0010010 => 0100100 => 15
0010011 => 1100100 => 31
0010100 => 0010100 => 11
0010101 => 1010100 => 26
0010110 => 0110100 => 22
0010111 => 1110100 => 36
0011000 => 0001100 => 8
0011001 => 1001100 => 22
0011010 => 0101100 => 18
0011011 => 1101100 => 31
0011100 => 0011100 => 15
0011101 => 1011100 => 27
0011110 => 0111100 => 24
0011111 => 1111100 => 35
0100000 => 0000010 => 1
0100001 => 1000010 => 17
0100010 => 0100010 => 12
0100011 => 1100010 => 27
0100100 => 0010010 => 8
0100101 => 1010010 => 22
0100110 => 0110010 => 18
0100111 => 1110010 => 31
0101000 => 0001010 => 5
0101001 => 1001010 => 18
0101010 => 0101010 => 14
0101011 => 1101010 => 26
0101100 => 0011010 => 11
0101101 => 1011010 => 22
0101110 => 0111010 => 19
0101111 => 1111010 => 29
0110000 => 0000110 => 3
0110001 => 1000110 => 15
0110010 => 0100110 => 11
0110011 => 1100110 => 22
0110100 => 0010110 => 8
0110101 => 1010110 => 18
0110110 => 0110110 => 15
0110111 => 1110110 => 24
0111000 => 0001110 => 6
0111001 => 1001110 => 15
0111010 => 0101110 => 12
0111011 => 1101110 => 20
0111100 => 0011110 => 10
0111101 => 1011110 => 17
0111110 => 0111110 => 15
0111111 => 1111110 => 21
1000000 => 0000001 => 0
1000001 => 1000001 => 15
1000010 => 0100001 => 10
1000011 => 1100001 => 24
1000100 => 0010001 => 6
1000101 => 1010001 => 19
1000110 => 0110001 => 15
1000111 => 1110001 => 27
1001000 => 0001001 => 3
1001001 => 1001001 => 15
1001010 => 0101001 => 11
1001011 => 1101001 => 22
1001100 => 0011001 => 8
1001101 => 1011001 => 18
1001110 => 0111001 => 15
1001111 => 1111001 => 24
1010000 => 0000101 => 1
1010001 => 1000101 => 12
1010010 => 0100101 => 8
1010011 => 1100101 => 18
1010100 => 0010101 => 5
1010101 => 1010101 => 14
1010110 => 0110101 => 11
1010111 => 1110101 => 19
1011000 => 0001101 => 3
1011001 => 1001101 => 11
1011010 => 0101101 => 8
1011011 => 1101101 => 15
1011100 => 0011101 => 6
1011101 => 1011101 => 12
1011110 => 0111101 => 10
1011111 => 1111101 => 15
1100000 => 0000011 => 0
1100001 => 1000011 => 10
1100010 => 0100011 => 6
1100011 => 1100011 => 15
1100100 => 0010011 => 3
1100101 => 1010011 => 11
1100110 => 0110011 => 8
1100111 => 1110011 => 15
1101000 => 0001011 => 1
1101001 => 1001011 => 8
1101010 => 0101011 => 5
1101011 => 1101011 => 11
1101100 => 0011011 => 3
1101101 => 1011011 => 8
1101110 => 0111011 => 6
1101111 => 1111011 => 10
1110000 => 0000111 => 0
1110001 => 1000111 => 6
1110010 => 0100111 => 3
1110011 => 1100111 => 8
1110100 => 0010111 => 1
1110101 => 1010111 => 5
1110110 => 0110111 => 3
1110111 => 1110111 => 6
1111000 => 0001111 => 0
1111001 => 1001111 => 3
1111010 => 0101111 => 1
1111011 => 1101111 => 3
1111100 => 0011111 => 0
1111101 => 1011111 => 1
1111110 => 0111111 => 0
1111111 => 1111111 => 0
00000000 => 00000000 => 0
00000001 => 10000000 => 28
00000010 => 01000000 => 21
00000011 => 11000000 => 48
00000100 => 00100000 => 15
00000101 => 10100000 => 41
00000110 => 01100000 => 35
00000111 => 11100000 => 60
00001000 => 00010000 => 10
00001001 => 10010000 => 35
00001010 => 01010000 => 29
00001011 => 11010000 => 53
00001100 => 00110000 => 24
00001101 => 10110000 => 47
00001110 => 01110000 => 42
00001111 => 11110000 => 64
00010000 => 00001000 => 6
00010001 => 10001000 => 30
00010010 => 01001000 => 24
00010011 => 11001000 => 47
00010100 => 00101000 => 19
00010101 => 10101000 => 41
00010110 => 01101000 => 36
00010111 => 11101000 => 57
00011000 => 00011000 => 15
00011001 => 10011000 => 36
00011010 => 01011000 => 31
00011011 => 11011000 => 51
00011100 => 00111000 => 27
00011101 => 10111000 => 46
00011110 => 01111000 => 42
00011111 => 11111000 => 60
00100000 => 00000100 => 3
00100001 => 10000100 => 26
00100010 => 01000100 => 20
00100011 => 11000100 => 42
00100100 => 00100100 => 15
00100101 => 10100100 => 36
00100110 => 01100100 => 31
00100111 => 11100100 => 51
00101000 => 00010100 => 11
00101001 => 10010100 => 31
00101010 => 01010100 => 26
00101011 => 11010100 => 45
00101100 => 00110100 => 22
00101101 => 10110100 => 40
00101110 => 01110100 => 36
00101111 => 11110100 => 53
00110000 => 00001100 => 8
00110001 => 10001100 => 27
00110010 => 01001100 => 22
00110011 => 11001100 => 40
00110100 => 00101100 => 18
00110101 => 10101100 => 35
00110110 => 01101100 => 31
00110111 => 11101100 => 47
00111000 => 00011100 => 15
00111001 => 10011100 => 31
00111010 => 01011100 => 27
00111011 => 11011100 => 42
00111100 => 00111100 => 24
00111101 => 10111100 => 38
00111110 => 01111100 => 35
00111111 => 11111100 => 48
01000000 => 00000010 => 1
01000001 => 10000010 => 23
01000010 => 01000010 => 17
01000011 => 11000010 => 38
01000100 => 00100010 => 12
01000101 => 10100010 => 32
01000110 => 01100010 => 27
01000111 => 11100010 => 46
01001000 => 00010010 => 8
01001001 => 10010010 => 27
01001010 => 01010010 => 22
01001011 => 11010010 => 40
01001100 => 00110010 => 18
01001101 => 10110010 => 35
01001110 => 01110010 => 31
01001111 => 11110010 => 47
01010000 => 00001010 => 5
01010001 => 10001010 => 23
01010010 => 01001010 => 18
01010011 => 11001010 => 35
01010100 => 00101010 => 14
01010101 => 10101010 => 30
01010110 => 01101010 => 26
01010111 => 11101010 => 41
01011000 => 00011010 => 11
01011001 => 10011010 => 26
01011010 => 01011010 => 22
01011011 => 11011010 => 36
01011100 => 00111010 => 19
01011101 => 10111010 => 32
01011110 => 01111010 => 29
01011111 => 11111010 => 41
01100000 => 00000110 => 3
01100001 => 10000110 => 20
01100010 => 01000110 => 15
01100011 => 11000110 => 31
01100100 => 00100110 => 11
01100101 => 10100110 => 26
01100110 => 01100110 => 22
01100111 => 11100110 => 36
01101000 => 00010110 => 8
01101001 => 10010110 => 22
01101010 => 01010110 => 18
01101011 => 11010110 => 31
01101100 => 00110110 => 15
01101101 => 10110110 => 27
01101110 => 01110110 => 24
01101111 => 11110110 => 35
01110000 => 00001110 => 6
01110001 => 10001110 => 19
01110010 => 01001110 => 15
01110011 => 11001110 => 27
01110100 => 00101110 => 12
01110101 => 10101110 => 23
01110110 => 01101110 => 20
01110111 => 11101110 => 30
01111000 => 00011110 => 10
01111001 => 10011110 => 20
01111010 => 01011110 => 17
01111011 => 11011110 => 26
01111100 => 00111110 => 15
01111101 => 10111110 => 23
01111110 => 01111110 => 21
01111111 => 11111110 => 28
10000000 => 00000001 => 0
10000001 => 10000001 => 21
10000010 => 01000001 => 15
10000011 => 11000001 => 35
10000100 => 00100001 => 10
10000101 => 10100001 => 29
10000110 => 01100001 => 24
10000111 => 11100001 => 42
10001000 => 00010001 => 6
10001001 => 10010001 => 24
10001010 => 01010001 => 19
10001011 => 11010001 => 36
10001100 => 00110001 => 15
10001101 => 10110001 => 31
10001110 => 01110001 => 27
10001111 => 11110001 => 42
10010000 => 00001001 => 3
10010001 => 10001001 => 20
10010010 => 01001001 => 15
10010011 => 11001001 => 31
10010100 => 00101001 => 11
10010101 => 10101001 => 26
10010110 => 01101001 => 22
10010111 => 11101001 => 36
10011000 => 00011001 => 8
10011001 => 10011001 => 22
10011010 => 01011001 => 18
10011011 => 11011001 => 31
10011100 => 00111001 => 15
10011101 => 10111001 => 27
10011110 => 01111001 => 24
10011111 => 11111001 => 35
10100000 => 00000101 => 1
10100001 => 10000101 => 17
10100010 => 01000101 => 12
10100011 => 11000101 => 27
10100100 => 00100101 => 8
10100101 => 10100101 => 22
10100110 => 01100101 => 18
10100111 => 11100101 => 31
10101000 => 00010101 => 5
10101001 => 10010101 => 18
10101010 => 01010101 => 14
10101011 => 11010101 => 26
10101100 => 00110101 => 11
10101101 => 10110101 => 22
10101110 => 01110101 => 19
10101111 => 11110101 => 29
10110000 => 00001101 => 3
10110001 => 10001101 => 15
10110010 => 01001101 => 11
10110011 => 11001101 => 22
10110100 => 00101101 => 8
10110101 => 10101101 => 18
10110110 => 01101101 => 15
10110111 => 11101101 => 24
10111000 => 00011101 => 6
10111001 => 10011101 => 15
10111010 => 01011101 => 12
10111011 => 11011101 => 20
10111100 => 00111101 => 10
10111101 => 10111101 => 17
10111110 => 01111101 => 15
10111111 => 11111101 => 21
11000000 => 00000011 => 0
11000001 => 10000011 => 15
11000010 => 01000011 => 10
11000011 => 11000011 => 24
11000100 => 00100011 => 6
11000101 => 10100011 => 19
11000110 => 01100011 => 15
11000111 => 11100011 => 27
11001000 => 00010011 => 3
11001001 => 10010011 => 15
11001010 => 01010011 => 11
11001011 => 11010011 => 22
11001100 => 00110011 => 8
11001101 => 10110011 => 18
11001110 => 01110011 => 15
11001111 => 11110011 => 24
11010000 => 00001011 => 1
11010001 => 10001011 => 12
11010010 => 01001011 => 8
11010011 => 11001011 => 18
11010100 => 00101011 => 5
11010101 => 10101011 => 14
11010110 => 01101011 => 11
11010111 => 11101011 => 19
11011000 => 00011011 => 3
11011001 => 10011011 => 11
11011010 => 01011011 => 8
11011011 => 11011011 => 15
11011100 => 00111011 => 6
11011101 => 10111011 => 12
11011110 => 01111011 => 10
11011111 => 11111011 => 15
11100000 => 00000111 => 0
11100001 => 10000111 => 10
11100010 => 01000111 => 6
11100011 => 11000111 => 15
11100100 => 00100111 => 3
11100101 => 10100111 => 11
11100110 => 01100111 => 8
11100111 => 11100111 => 15
11101000 => 00010111 => 1
11101001 => 10010111 => 8
11101010 => 01010111 => 5
11101011 => 11010111 => 11
11101100 => 00110111 => 3
11101101 => 10110111 => 8
11101110 => 01110111 => 6
11101111 => 11110111 => 10
11110000 => 00001111 => 0
11110001 => 10001111 => 6
11110010 => 01001111 => 3
11110011 => 11001111 => 8
11110100 => 00101111 => 1
11110101 => 10101111 => 5
11110110 => 01101111 => 3
11110111 => 11101111 => 6
11111000 => 00011111 => 0
11111001 => 10011111 => 3
11111010 => 01011111 => 1
11111011 => 11011111 => 3
11111100 => 00111111 => 0
11111101 => 10111111 => 1
11111110 => 01111111 => 0
11111111 => 11111111 => 0
000000000 => 000000000 => 0
000000001 => 100000000 => 36
000000010 => 010000000 => 28
000000011 => 110000000 => 63
000000100 => 001000000 => 21
000000101 => 101000000 => 55
000000110 => 011000000 => 48
000000111 => 111000000 => 81
000001000 => 000100000 => 15
000001001 => 100100000 => 48
000001010 => 010100000 => 41
000001011 => 110100000 => 73
000001100 => 001100000 => 35
000001101 => 101100000 => 66
000001110 => 011100000 => 60
000001111 => 111100000 => 90
000010000 => 000010000 => 10
000010001 => 100010000 => 42
000010010 => 010010000 => 35
000010011 => 110010000 => 66
000010100 => 001010000 => 29
000010101 => 101010000 => 59
000010110 => 011010000 => 53
000010111 => 111010000 => 82
000011000 => 000110000 => 24
000011001 => 100110000 => 53
000011010 => 010110000 => 47
000011011 => 110110000 => 75
000011100 => 001110000 => 42
000011101 => 101110000 => 69
000011110 => 011110000 => 64
000011111 => 111110000 => 90
000100000 => 000001000 => 6
000100001 => 100001000 => 37
000100010 => 010001000 => 30
000100011 => 110001000 => 60
000100100 => 001001000 => 24
000100101 => 101001000 => 53
000100110 => 011001000 => 47
000100111 => 111001000 => 75
000101000 => 000101000 => 19
000101001 => 100101000 => 47
000101010 => 010101000 => 41
000101011 => 110101000 => 68
000101100 => 001101000 => 36
000101101 => 101101000 => 62
000101110 => 011101000 => 57
000101111 => 111101000 => 82
000110000 => 000011000 => 15
000110001 => 100011000 => 42
000110010 => 010011000 => 36
000110011 => 110011000 => 62
000110100 => 001011000 => 31
000110101 => 101011000 => 56
000110110 => 011011000 => 51
000110111 => 111011000 => 75
000111000 => 000111000 => 27
000111001 => 100111000 => 51
000111010 => 010111000 => 46
000111011 => 110111000 => 69
000111100 => 001111000 => 42
000111101 => 101111000 => 64
000111110 => 011111000 => 60
000111111 => 111111000 => 81
001000000 => 000000100 => 3
001000001 => 100000100 => 33
001000010 => 010000100 => 26
001000011 => 110000100 => 55
001000100 => 001000100 => 20
001000101 => 101000100 => 48
001000110 => 011000100 => 42
001000111 => 111000100 => 69
001001000 => 000100100 => 15
001001001 => 100100100 => 42
001001010 => 010100100 => 36
001001011 => 110100100 => 62
001001100 => 001100100 => 31
001001101 => 101100100 => 56
001001110 => 011100100 => 51
001001111 => 111100100 => 75
001010000 => 000010100 => 11
001010001 => 100010100 => 37
001010010 => 010010100 => 31
001010011 => 110010100 => 56
001010100 => 001010100 => 26
001010101 => 101010100 => 50
001010110 => 011010100 => 45
001010111 => 111010100 => 68
001011000 => 000110100 => 22
001011001 => 100110100 => 45
001011010 => 010110100 => 40
001011011 => 110110100 => 62
001011100 => 001110100 => 36
001011101 => 101110100 => 57
001011110 => 011110100 => 53
001011111 => 111110100 => 73
001100000 => 000001100 => 8
001100001 => 100001100 => 33
001100010 => 010001100 => 27
001100011 => 110001100 => 51
001100100 => 001001100 => 22
001100101 => 101001100 => 45
001100110 => 011001100 => 40
001100111 => 111001100 => 62
001101000 => 000101100 => 18
001101001 => 100101100 => 40
001101010 => 010101100 => 35
001101011 => 110101100 => 56
001101100 => 001101100 => 31
001101101 => 101101100 => 51
001101110 => 011101100 => 47
001101111 => 111101100 => 66
001110000 => 000011100 => 15
001110001 => 100011100 => 36
001110010 => 010011100 => 31
001110011 => 110011100 => 51
001110100 => 001011100 => 27
001110101 => 101011100 => 46
001110110 => 011011100 => 42
001110111 => 111011100 => 60
001111000 => 000111100 => 24
001111001 => 100111100 => 42
001111010 => 010111100 => 38
001111011 => 110111100 => 55
001111100 => 001111100 => 35
001111101 => 101111100 => 51
001111110 => 011111100 => 48
001111111 => 111111100 => 63
010000000 => 000000010 => 1
010000001 => 100000010 => 30
010000010 => 010000010 => 23
010000011 => 110000010 => 51
010000100 => 001000010 => 17
010000101 => 101000010 => 44
010000110 => 011000010 => 38
010000111 => 111000010 => 64
010001000 => 000100010 => 12
010001001 => 100100010 => 38
010001010 => 010100010 => 32
010001011 => 110100010 => 57
010001100 => 001100010 => 27
010001101 => 101100010 => 51
010001110 => 011100010 => 46
010001111 => 111100010 => 69
010010000 => 000010010 => 8
010010001 => 100010010 => 33
010010010 => 010010010 => 27
010010011 => 110010010 => 51
010010100 => 001010010 => 22
010010101 => 101010010 => 45
010010110 => 011010010 => 40
010010111 => 111010010 => 62
010011000 => 000110010 => 18
010011001 => 100110010 => 40
010011010 => 010110010 => 35
010011011 => 110110010 => 56
010011100 => 001110010 => 31
010011101 => 101110010 => 51
010011110 => 011110010 => 47
010011111 => 111110010 => 66
010100000 => 000001010 => 5
010100001 => 100001010 => 29
010100010 => 010001010 => 23
010100011 => 110001010 => 46
010100100 => 001001010 => 18
010100101 => 101001010 => 40
010100110 => 011001010 => 35
010100111 => 111001010 => 56
010101000 => 000101010 => 14
010101001 => 100101010 => 35
010101010 => 010101010 => 30
010101011 => 110101010 => 50
010101100 => 001101010 => 26
010101101 => 101101010 => 45
010101110 => 011101010 => 41
010101111 => 111101010 => 59
010110000 => 000011010 => 11
010110001 => 100011010 => 31
010110010 => 010011010 => 26
010110011 => 110011010 => 45
010110100 => 001011010 => 22
010110101 => 101011010 => 40
010110110 => 011011010 => 36
010110111 => 111011010 => 53
010111000 => 000111010 => 19
010111001 => 100111010 => 36
010111010 => 010111010 => 32
010111011 => 110111010 => 48
010111100 => 001111010 => 29
010111101 => 101111010 => 44
010111110 => 011111010 => 41
010111111 => 111111010 => 55
011000000 => 000000110 => 3
011000001 => 100000110 => 26
011000010 => 010000110 => 20
011000011 => 110000110 => 42
011000100 => 001000110 => 15
011000101 => 101000110 => 36
011000110 => 011000110 => 31
011000111 => 111000110 => 51
011001000 => 000100110 => 11
011001001 => 100100110 => 31
011001010 => 010100110 => 26
011001011 => 110100110 => 45
011001100 => 001100110 => 22
011001101 => 101100110 => 40
011001110 => 011100110 => 36
011001111 => 111100110 => 53
011010000 => 000010110 => 8
011010001 => 100010110 => 27
011010010 => 010010110 => 22
011010011 => 110010110 => 40
011010100 => 001010110 => 18
011010101 => 101010110 => 35
011010110 => 011010110 => 31
011010111 => 111010110 => 47
011011000 => 000110110 => 15
011011001 => 100110110 => 31
011011010 => 010110110 => 27
011011011 => 110110110 => 42
011011100 => 001110110 => 24
011011101 => 101110110 => 38
011011110 => 011110110 => 35
011011111 => 111110110 => 48
011100000 => 000001110 => 6
011100001 => 100001110 => 24
011100010 => 010001110 => 19
011100011 => 110001110 => 36
011100100 => 001001110 => 15
011100101 => 101001110 => 31
011100110 => 011001110 => 27
011100111 => 111001110 => 42
011101000 => 000101110 => 12
011101001 => 100101110 => 27
011101010 => 010101110 => 23
011101011 => 110101110 => 37
011101100 => 001101110 => 20
011101101 => 101101110 => 33
011101110 => 011101110 => 30
011101111 => 111101110 => 42
011110000 => 000011110 => 10
011110001 => 100011110 => 24
011110010 => 010011110 => 20
011110011 => 110011110 => 33
011110100 => 001011110 => 17
011110101 => 101011110 => 29
011110110 => 011011110 => 26
011110111 => 111011110 => 37
011111000 => 000111110 => 15
011111001 => 100111110 => 26
011111010 => 010111110 => 23
011111011 => 110111110 => 33
011111100 => 001111110 => 21
011111101 => 101111110 => 30
011111110 => 011111110 => 28
011111111 => 111111110 => 36
100000000 => 000000001 => 0
100000001 => 100000001 => 28
100000010 => 010000001 => 21
100000011 => 110000001 => 48
100000100 => 001000001 => 15
100000101 => 101000001 => 41
100000110 => 011000001 => 35
100000111 => 111000001 => 60
100001000 => 000100001 => 10
100001001 => 100100001 => 35
100001010 => 010100001 => 29
100001011 => 110100001 => 53
100001100 => 001100001 => 24
100001101 => 101100001 => 47
100001110 => 011100001 => 42
100001111 => 111100001 => 64
100010000 => 000010001 => 6
100010001 => 100010001 => 30
100010010 => 010010001 => 24
100010011 => 110010001 => 47
100010100 => 001010001 => 19
100010101 => 101010001 => 41
100010110 => 011010001 => 36
100010111 => 111010001 => 57
100011000 => 000110001 => 15
100011001 => 100110001 => 36
100011010 => 010110001 => 31
100011011 => 110110001 => 51
100011100 => 001110001 => 27
100011101 => 101110001 => 46
100011110 => 011110001 => 42
100011111 => 111110001 => 60
100100000 => 000001001 => 3
100100001 => 100001001 => 26
100100010 => 010001001 => 20
100100011 => 110001001 => 42
100100100 => 001001001 => 15
100100101 => 101001001 => 36
100100110 => 011001001 => 31
100100111 => 111001001 => 51
100101000 => 000101001 => 11
100101001 => 100101001 => 31
100101010 => 010101001 => 26
100101011 => 110101001 => 45
100101100 => 001101001 => 22
100101101 => 101101001 => 40
100101110 => 011101001 => 36
100101111 => 111101001 => 53
100110000 => 000011001 => 8
100110001 => 100011001 => 27
100110010 => 010011001 => 22
100110011 => 110011001 => 40
100110100 => 001011001 => 18
100110101 => 101011001 => 35
100110110 => 011011001 => 31
100110111 => 111011001 => 47
100111000 => 000111001 => 15
100111001 => 100111001 => 31
100111010 => 010111001 => 27
100111011 => 110111001 => 42
100111100 => 001111001 => 24
100111101 => 101111001 => 38
100111110 => 011111001 => 35
100111111 => 111111001 => 48
101000000 => 000000101 => 1
101000001 => 100000101 => 23
101000010 => 010000101 => 17
101000011 => 110000101 => 38
101000100 => 001000101 => 12
101000101 => 101000101 => 32
101000110 => 011000101 => 27
101000111 => 111000101 => 46
101001000 => 000100101 => 8
101001001 => 100100101 => 27
101001010 => 010100101 => 22
101001011 => 110100101 => 40
101001100 => 001100101 => 18
101001101 => 101100101 => 35
101001110 => 011100101 => 31
101001111 => 111100101 => 47
101010000 => 000010101 => 5
101010001 => 100010101 => 23
101010010 => 010010101 => 18
101010011 => 110010101 => 35
101010100 => 001010101 => 14
101010101 => 101010101 => 30
101010110 => 011010101 => 26
101010111 => 111010101 => 41
101011000 => 000110101 => 11
101011001 => 100110101 => 26
101011010 => 010110101 => 22
101011011 => 110110101 => 36
101011100 => 001110101 => 19
101011101 => 101110101 => 32
101011110 => 011110101 => 29
101011111 => 111110101 => 41
101100000 => 000001101 => 3
101100001 => 100001101 => 20
101100010 => 010001101 => 15
101100011 => 110001101 => 31
101100100 => 001001101 => 11
101100101 => 101001101 => 26
101100110 => 011001101 => 22
101100111 => 111001101 => 36
101101000 => 000101101 => 8
101101001 => 100101101 => 22
101101010 => 010101101 => 18
101101011 => 110101101 => 31
101101100 => 001101101 => 15
101101101 => 101101101 => 27
101101110 => 011101101 => 24
101101111 => 111101101 => 35
101110000 => 000011101 => 6
101110001 => 100011101 => 19
101110010 => 010011101 => 15
101110011 => 110011101 => 27
101110100 => 001011101 => 12
101110101 => 101011101 => 23
101110110 => 011011101 => 20
101110111 => 111011101 => 30
101111000 => 000111101 => 10
101111001 => 100111101 => 20
101111010 => 010111101 => 17
101111011 => 110111101 => 26
101111100 => 001111101 => 15
101111101 => 101111101 => 23
101111110 => 011111101 => 21
101111111 => 111111101 => 28
110000000 => 000000011 => 0
110000001 => 100000011 => 21
110000010 => 010000011 => 15
110000011 => 110000011 => 35
110000100 => 001000011 => 10
110000101 => 101000011 => 29
110000110 => 011000011 => 24
110000111 => 111000011 => 42
110001000 => 000100011 => 6
110001001 => 100100011 => 24
110001010 => 010100011 => 19
110001011 => 110100011 => 36
110001100 => 001100011 => 15
110001101 => 101100011 => 31
110001110 => 011100011 => 27
110001111 => 111100011 => 42
110010000 => 000010011 => 3
110010001 => 100010011 => 20
110010010 => 010010011 => 15
110010011 => 110010011 => 31
110010100 => 001010011 => 11
110010101 => 101010011 => 26
110010110 => 011010011 => 22
110010111 => 111010011 => 36
110011000 => 000110011 => 8
110011001 => 100110011 => 22
110011010 => 010110011 => 18
110011011 => 110110011 => 31
110011100 => 001110011 => 15
110011101 => 101110011 => 27
110011110 => 011110011 => 24
110011111 => 111110011 => 35
110100000 => 000001011 => 1
110100001 => 100001011 => 17
110100010 => 010001011 => 12
110100011 => 110001011 => 27
110100100 => 001001011 => 8
110100101 => 101001011 => 22
110100110 => 011001011 => 18
110100111 => 111001011 => 31
110101000 => 000101011 => 5
110101001 => 100101011 => 18
110101010 => 010101011 => 14
110101011 => 110101011 => 26
110101100 => 001101011 => 11
110101101 => 101101011 => 22
110101110 => 011101011 => 19
110101111 => 111101011 => 29
110110000 => 000011011 => 3
110110001 => 100011011 => 15
110110010 => 010011011 => 11
110110011 => 110011011 => 22
110110100 => 001011011 => 8
110110101 => 101011011 => 18
110110110 => 011011011 => 15
110110111 => 111011011 => 24
110111000 => 000111011 => 6
110111001 => 100111011 => 15
110111010 => 010111011 => 12
110111011 => 110111011 => 20
110111100 => 001111011 => 10
110111101 => 101111011 => 17
110111110 => 011111011 => 15
110111111 => 111111011 => 21
111000000 => 000000111 => 0
111000001 => 100000111 => 15
111000010 => 010000111 => 10
111000011 => 110000111 => 24
111000100 => 001000111 => 6
111000101 => 101000111 => 19
111000110 => 011000111 => 15
111000111 => 111000111 => 27
111001000 => 000100111 => 3
111001001 => 100100111 => 15
111001010 => 010100111 => 11
111001011 => 110100111 => 22
111001100 => 001100111 => 8
111001101 => 101100111 => 18
111001110 => 011100111 => 15
111001111 => 111100111 => 24
111010000 => 000010111 => 1
111010001 => 100010111 => 12
111010010 => 010010111 => 8
111010011 => 110010111 => 18
111010100 => 001010111 => 5
111010101 => 101010111 => 14
111010110 => 011010111 => 11
111010111 => 111010111 => 19
111011000 => 000110111 => 3
111011001 => 100110111 => 11
111011010 => 010110111 => 8
111011011 => 110110111 => 15
111011100 => 001110111 => 6
111011101 => 101110111 => 12
111011110 => 011110111 => 10
111011111 => 111110111 => 15
111100000 => 000001111 => 0
111100001 => 100001111 => 10
111100010 => 010001111 => 6
111100011 => 110001111 => 15
111100100 => 001001111 => 3
111100101 => 101001111 => 11
111100110 => 011001111 => 8
111100111 => 111001111 => 15
111101000 => 000101111 => 1
111101001 => 100101111 => 8
111101010 => 010101111 => 5
111101011 => 110101111 => 11
111101100 => 001101111 => 3
111101101 => 101101111 => 8
111101110 => 011101111 => 6
111101111 => 111101111 => 10
111110000 => 000011111 => 0
111110001 => 100011111 => 6
111110010 => 010011111 => 3
111110011 => 110011111 => 8
111110100 => 001011111 => 1
111110101 => 101011111 => 5
111110110 => 011011111 => 3
111110111 => 111011111 => 6
111111000 => 000111111 => 0
111111001 => 100111111 => 3
111111010 => 010111111 => 1
111111011 => 110111111 => 3
111111100 => 001111111 => 0
111111101 => 101111111 => 1
111111110 => 011111111 => 0
111111111 => 111111111 => 0
1010111000 => 0001110101 => 19
1011010100 => 0010101101 => 18
1011011000 => 0001101101 => 15
1011100100 => 0010011101 => 15
1011101000 => 0001011101 => 12
1011110000 => 0000111101 => 10
1100111000 => 0001110011 => 15
1101010100 => 0010101011 => 14
1101011000 => 0001101011 => 11
1101100100 => 0010011011 => 11
1101101000 => 0001011011 => 8
1101110000 => 0000111011 => 6
1110010100 => 0010100111 => 11
1110011000 => 0001100111 => 8
1110100100 => 0010010111 => 8
1110101000 => 0001010111 => 5
1110110000 => 0000110111 => 3
1111000100 => 0010001111 => 6
1111001000 => 0001001111 => 3
1111010000 => 0000101111 => 1
1111100000 => 0000011111 => 0
1111111000 => 0001111111 => 0
1111110000 => 0000111111 => 0
1111101000 => 0001011111 => 1
1111100100 => 0010011111 => 3
1111011000 => 0001101111 => 3
1111010100 => 0010101111 => 5
1111000000 => 0000001111 => 0
1110111000 => 0001110111 => 6
1110100000 => 0000010111 => 1
1110010000 => 0000100111 => 3
1110001000 => 0001000111 => 6
1110000100 => 0010000111 => 10
1110000000 => 0000000111 => 0
1101111000 => 0001111011 => 10
1101100000 => 0000011011 => 3
1101010000 => 0000101011 => 5
1101001000 => 0001001011 => 8
1101000100 => 0010001011 => 12
1101000000 => 0000001011 => 1
1100110000 => 0000110011 => 8
1100101000 => 0001010011 => 11
1100100100 => 0010010011 => 15
1100100000 => 0000010011 => 3
1100011000 => 0001100011 => 15
1100010100 => 0010100011 => 19
1100010000 => 0000100011 => 6
1100001000 => 0001000011 => 10
1100000100 => 0010000011 => 15
1100000000 => 0000000011 => 0
1011111000 => 0001111101 => 15
1011100000 => 0000011101 => 6
1011010000 => 0000101101 => 8
1011001000 => 0001001101 => 11
1011000100 => 0010001101 => 15
1011000000 => 0000001101 => 3
1010110000 => 0000110101 => 11
1010101000 => 0001010101 => 14
1010100100 => 0010010101 => 18
1010100000 => 0000010101 => 5
1010011000 => 0001100101 => 18
1010010100 => 0010100101 => 22
1010010000 => 0000100101 => 8
1010001000 => 0001000101 => 12
1010000100 => 0010000101 => 17
1010000000 => 0000000101 => 1
1001111000 => 0001111001 => 24
1001110000 => 0000111001 => 15
1001101000 => 0001011001 => 18
1001100100 => 0010011001 => 22
1001100000 => 0000011001 => 8
1001011000 => 0001101001 => 22
1001010100 => 0010101001 => 26
1001010000 => 0000101001 => 11
1001001000 => 0001001001 => 15
1001000100 => 0010001001 => 20
1001000000 => 0000001001 => 3
1000111000 => 0001110001 => 27
1000110100 => 0010110001 => 31
1000110000 => 0000110001 => 15
1000101000 => 0001010001 => 19
1000100100 => 0010010001 => 24
1000100000 => 0000010001 => 6
1000011000 => 0001100001 => 24
1000010100 => 0010100001 => 29
1000010000 => 0000100001 => 10
1000001000 => 0001000001 => 15
1000000100 => 0010000001 => 21
1000000000 => 0000000001 => 0
0000000000 => 0000000000 => 0
0000011000 => 0001100000 => 35
0001100000 => 0000011000 => 15
0001111000 => 0001111000 => 42
0001001000 => 0001001000 => 24
0110000000 => 0000000110 => 3
0110011000 => 0001100110 => 22
0111100000 => 0000011110 => 10
0111111000 => 0001111110 => 21
0111001000 => 0001001110 => 15
0100100000 => 0000010010 => 8
0100111000 => 0001110010 => 31
0100001000 => 0001000010 => 17
0101101000 => 0001011010 => 22
0010101000 => 0001010100 => 26
0010100100 => 0010010100 => 31
0010010100 => 0010100100 => 36
0011010100 => 0010101100 => 35
0001010100 => 0010101000 => 41
0101010100 => 0010101010 => 30
0010100000 => 0000010100 => 11
0010000100 => 0010000100 => 26
0000010100 => 0010100000 => 41
0111010100 => 0010101110 => 23
0000000100 => 0010000000 => 28
0010111000 => 0001110100 => 36
0011011000 => 0001101100 => 31
0011100100 => 0010011100 => 31
0011101000 => 0001011100 => 27
0011110000 => 0000111100 => 24
0101011000 => 0001101010 => 26
0101100100 => 0010011010 => 26
0101110000 => 0000111010 => 19
0110010100 => 0010100110 => 26
0110100100 => 0010010110 => 22
0110101000 => 0001010110 => 18
0110110000 => 0000110110 => 15
0111000100 => 0010001110 => 19
0111010000 => 0000101110 => 12
0100000000 => 0000000010 => 1
0101111000 => 0001111010 => 29
0110111000 => 0001110110 => 24
0111011000 => 0001101110 => 20
0111100100 => 0010011110 => 20
0111101000 => 0001011110 => 17
0111110000 => 0000111110 => 15
0100000100 => 0010000010 => 23
0011111000 => 0001111100 => 35
0000110100 => 0010110000 => 47
0101000000 => 0000001010 => 5
0001010000 => 0000101000 => 19
0100010000 => 0000100010 => 12
0001000100 => 0010001000 => 30
0111000000 => 0000001110 => 6
0010000000 => 0000000100 => 3
0110100000 => 0000010110 => 8
0000100100 => 0010010000 => 35
0011000000 => 0000001100 => 8
0010110000 => 0000110100 => 22
0000001000 => 0001000000 => 21
0000101000 => 0001010000 => 29
0010001000 => 0001000100 => 20
0011000100 => 0010001100 => 27
0001100100 => 0010011000 => 36
0101001000 => 0001001010 => 18
0101010000 => 0000101010 => 14
0010010000 => 0000100100 => 15
0100101000 => 0001010010 => 22
0001000000 => 0000001000 => 6
0100011000 => 0001100010 => 27
0010011000 => 0001100100 => 31
0001011000 => 0001101000 => 36
0000100000 => 0000010000 => 10
0000110000 => 0000110000 => 24
0101100000 => 0000011010 => 11
0000111000 => 0001110000 => 42
0000010000 => 0000100000 => 15
0011100000 => 0000011100 => 15
0101000100 => 0010001010 => 23
0100010100 => 0010100010 => 32
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
3,1 4,2,0,2 5,3,0,4,0,1,2,0,1 6,4,0,6,0,2,4,0,4,0,2,2,0,0,0,2 7,5,0,8,0,3,6,0,7,0,4,5,2,0,1,8,0,0,2,2,0,0,1,0,2,0,0,1
$F_{1} = 2$
$F_{2} = 3 + q$
$F_{3} = 4 + 2\ q + 2\ q^{3}$
$F_{4} = 5 + 3\ q + 4\ q^{3} + q^{5} + 2\ q^{6} + q^{8}$
$F_{5} = 6 + 4\ q + 6\ q^{3} + 2\ q^{5} + 4\ q^{6} + 4\ q^{8} + 2\ q^{10} + 2\ q^{11} + 2\ q^{15}$
$F_{6} = 7 + 5\ q + 8\ q^{3} + 3\ q^{5} + 6\ q^{6} + 7\ q^{8} + 4\ q^{10} + 5\ q^{11} + 2\ q^{12} + q^{14} + 8\ q^{15} + 2\ q^{18} + 2\ q^{19} + q^{22} + 2\ q^{24} + q^{27}$
$F_{7} = 8 + 6\ q + 10\ q^{3} + 4\ q^{5} + 8\ q^{6} + 10\ q^{8} + 6\ q^{10} + 8\ q^{11} + 4\ q^{12} + 2\ q^{14} + 16\ q^{15} + 2\ q^{17} + 6\ q^{18} + 4\ q^{19} + 2\ q^{20} + 2\ q^{21} + 6\ q^{22} + 6\ q^{24} + 2\ q^{26} + 4\ q^{27} + 2\ q^{29} + 4\ q^{31} + 2\ q^{35} + 2\ q^{36} + 2\ q^{42}$
$F_{8} = 9 + 7\ q + 12\ q^{3} + 5\ q^{5} + 10\ q^{6} + 13\ q^{8} + 8\ q^{10} + 11\ q^{11} + 6\ q^{12} + 3\ q^{14} + 24\ q^{15} + 4\ q^{17} + 10\ q^{18} + 7\ q^{19} + 6\ q^{20} + 4\ q^{21} + 12\ q^{22} + 4\ q^{23} + 10\ q^{24} + 8\ q^{26} + 11\ q^{27} + 2\ q^{28} + 4\ q^{29} + 3\ q^{30} + 12\ q^{31} + 2\ q^{32} + 9\ q^{35} + 8\ q^{36} + 2\ q^{38} + 3\ q^{40} + 4\ q^{41} + 6\ q^{42} + q^{45} + 2\ q^{46} + 4\ q^{47} + 2\ q^{48} + 2\ q^{51} + 2\ q^{53} + q^{57} + 2\ q^{60} + q^{64}$
$F_{9} = 10 + 8\ q + 14\ q^{3} + 6\ q^{5} + 12\ q^{6} + 16\ q^{8} + 10\ q^{10} + 14\ q^{11} + 8\ q^{12} + 4\ q^{14} + 32\ q^{15} + 6\ q^{17} + 14\ q^{18} + 10\ q^{19} + 10\ q^{20} + 6\ q^{21} + 18\ q^{22} + 8\ q^{23} + 16\ q^{24} + 16\ q^{26} + 20\ q^{27} + 4\ q^{28} + 8\ q^{29} + 8\ q^{30} + 24\ q^{31} + 4\ q^{32} + 6\ q^{33} + 18\ q^{35} + 20\ q^{36} + 4\ q^{37} + 6\ q^{38} + 12\ q^{40} + 8\ q^{41} + 18\ q^{42} + 2\ q^{44} + 8\ q^{45} + 6\ q^{46} + 10\ q^{47} + 8\ q^{48} + 2\ q^{50} + 14\ q^{51} + 8\ q^{53} + 4\ q^{55} + 6\ q^{56} + 4\ q^{57} + 2\ q^{59} + 6\ q^{60} + 6\ q^{62} + 2\ q^{63} + 4\ q^{64} + 4\ q^{66} + 2\ q^{68} + 4\ q^{69} + 2\ q^{73} + 4\ q^{75} + 2\ q^{81} + 2\ q^{82} + 2\ q^{90}$
Description
The inversion sum of a binary word.
A pair $a < b$ is an inversion of a binary word $w = w_1 \cdots w_n$ if $w_a = 1 > 0 = w_b$. The inversion sum is given by $\sum(b-a)$ over all inversions of $\pi$.
A pair $a < b$ is an inversion of a binary word $w = w_1 \cdots w_n$ if $w_a = 1 > 0 = w_b$. The inversion sum is given by $\sum(b-a)$ over all inversions of $\pi$.
Map
reverse
Description
Return the reversal of a binary word.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!