Identifier
- St001420: Binary words ⟶ ℤ
Values
=>
0=>0
1=>0
00=>0
01=>1
10=>1
11=>0
000=>0
001=>1
010=>1
011=>1
100=>1
101=>1
110=>1
111=>0
0000=>0
0001=>1
0010=>1
0011=>2
0100=>1
0101=>2
0110=>1
0111=>1
1000=>1
1001=>1
1010=>2
1011=>1
1100=>2
1101=>1
1110=>1
1111=>0
00000=>0
00001=>1
00010=>1
00011=>2
00100=>1
00101=>2
00110=>2
00111=>2
01000=>1
01001=>1
01010=>2
01011=>2
01100=>2
01101=>1
01110=>1
01111=>1
10000=>1
10001=>1
10010=>1
10011=>2
10100=>2
10101=>2
10110=>1
10111=>1
11000=>2
11001=>2
11010=>2
11011=>1
11100=>2
11101=>1
11110=>1
11111=>0
000000=>0
000001=>1
000010=>1
000011=>2
000100=>1
000101=>2
000110=>2
000111=>3
001000=>1
001001=>1
001010=>2
001011=>3
001100=>2
001101=>2
001110=>2
001111=>2
010000=>1
010001=>1
010010=>1
010011=>2
010100=>2
010101=>3
010110=>2
010111=>2
011000=>2
011001=>3
011010=>2
011011=>1
011100=>2
011101=>1
011110=>1
011111=>1
100000=>1
100001=>1
100010=>1
100011=>2
100100=>1
100101=>2
100110=>3
100111=>2
101000=>2
101001=>2
101010=>3
101011=>2
101100=>2
101101=>1
101110=>1
101111=>1
110000=>2
110001=>2
110010=>2
110011=>2
110100=>3
110101=>2
110110=>1
110111=>1
111000=>3
111001=>2
111010=>2
111011=>1
111100=>2
111101=>1
111110=>1
111111=>0
0000000=>0
0000001=>1
0000010=>1
0000011=>2
0000100=>1
0000101=>2
0000110=>2
0000111=>3
0001000=>1
0001001=>1
0001010=>2
0001011=>3
0001100=>2
0001101=>2
0001110=>3
0001111=>3
0010000=>1
0010001=>1
0010010=>1
0010011=>2
0010100=>2
0010101=>3
0010110=>3
0010111=>3
0011000=>2
0011001=>3
0011010=>2
0011011=>2
0011100=>2
0011101=>2
0011110=>2
0011111=>2
0100000=>1
0100001=>1
0100010=>1
0100011=>2
0100100=>1
0100101=>2
0100110=>3
0100111=>2
0101000=>2
0101001=>2
0101010=>3
0101011=>3
0101100=>2
0101101=>2
0101110=>2
0101111=>2
0110000=>2
0110001=>2
0110010=>3
0110011=>3
0110100=>3
0110101=>2
0110110=>1
0110111=>1
0111000=>3
0111001=>2
0111010=>2
0111011=>1
0111100=>2
0111101=>1
0111110=>1
0111111=>1
1000000=>1
1000001=>1
1000010=>1
1000011=>2
1000100=>1
1000101=>2
1000110=>2
1000111=>3
1001000=>1
1001001=>1
1001010=>2
1001011=>3
1001100=>3
1001101=>3
1001110=>2
1001111=>2
1010000=>2
1010001=>2
1010010=>2
1010011=>2
1010100=>3
1010101=>3
1010110=>2
1010111=>2
1011000=>2
1011001=>3
1011010=>2
1011011=>1
1011100=>2
1011101=>1
1011110=>1
1011111=>1
1100000=>2
1100001=>2
1100010=>2
1100011=>2
1100100=>2
1100101=>2
1100110=>3
1100111=>2
1101000=>3
1101001=>3
1101010=>3
1101011=>2
1101100=>2
1101101=>1
1101110=>1
1101111=>1
1110000=>3
1110001=>3
1110010=>2
1110011=>2
1110100=>3
1110101=>2
1110110=>1
1110111=>1
1111000=>3
1111001=>2
1111010=>2
1111011=>1
1111100=>2
1111101=>1
1111110=>1
1111111=>0
00000000=>0
00000001=>1
00000010=>1
00000011=>2
00000100=>1
00000101=>2
00000110=>2
00000111=>3
00001000=>1
00001001=>1
00001010=>2
00001011=>3
00001100=>2
00001101=>2
00001110=>3
00001111=>4
00010000=>1
00010001=>1
00010010=>1
00010011=>2
00010100=>2
00010101=>3
00010110=>3
00010111=>4
00011000=>2
00011001=>3
00011010=>2
00011011=>2
00011100=>3
00011101=>3
00011110=>3
00011111=>3
00100000=>1
00100001=>1
00100010=>1
00100011=>2
00100100=>1
00100101=>2
00100110=>3
00100111=>2
00101000=>2
00101001=>2
00101010=>3
00101011=>4
00101100=>3
00101101=>3
00101110=>3
00101111=>3
00110000=>2
00110001=>2
00110010=>3
00110011=>4
00110100=>3
00110101=>2
00110110=>2
00110111=>2
00111000=>3
00111001=>2
00111010=>2
00111011=>2
00111100=>2
00111101=>2
00111110=>2
00111111=>2
01000000=>1
01000001=>1
01000010=>1
01000011=>2
01000100=>1
01000101=>2
01000110=>2
01000111=>3
01001000=>1
01001001=>1
01001010=>2
01001011=>3
01001100=>3
01001101=>4
01001110=>2
01001111=>2
01010000=>2
01010001=>2
01010010=>2
01010011=>2
01010100=>3
01010101=>4
01010110=>3
01010111=>3
01011000=>2
01011001=>3
01011010=>2
01011011=>2
01011100=>2
01011101=>2
01011110=>2
01011111=>2
01100000=>2
01100001=>2
01100010=>2
01100011=>2
01100100=>3
01100101=>3
01100110=>3
01100111=>3
01101000=>3
01101001=>4
01101010=>3
01101011=>2
01101100=>2
01101101=>1
01101110=>1
01101111=>1
01110000=>3
01110001=>4
01110010=>2
01110011=>2
01110100=>3
01110101=>2
01110110=>1
01110111=>1
01111000=>3
01111001=>2
01111010=>2
01111011=>1
01111100=>2
01111101=>1
01111110=>1
01111111=>1
10000000=>1
10000001=>1
10000010=>1
10000011=>2
10000100=>1
10000101=>2
10000110=>2
10000111=>3
10001000=>1
10001001=>1
10001010=>2
10001011=>3
10001100=>2
10001101=>2
10001110=>4
10001111=>3
10010000=>1
10010001=>1
10010010=>1
10010011=>2
10010100=>2
10010101=>3
10010110=>4
10010111=>3
10011000=>3
10011001=>3
10011010=>3
10011011=>3
10011100=>2
10011101=>2
10011110=>2
10011111=>2
10100000=>2
10100001=>2
10100010=>2
10100011=>2
10100100=>2
10100101=>2
10100110=>3
10100111=>2
10101000=>3
10101001=>3
10101010=>4
10101011=>3
10101100=>2
10101101=>2
10101110=>2
10101111=>2
10110000=>2
10110001=>2
10110010=>4
10110011=>3
10110100=>3
10110101=>2
10110110=>1
10110111=>1
10111000=>3
10111001=>2
10111010=>2
10111011=>1
10111100=>2
10111101=>1
10111110=>1
10111111=>1
11000000=>2
11000001=>2
11000010=>2
11000011=>2
11000100=>2
11000101=>2
11000110=>2
11000111=>3
11001000=>2
11001001=>2
11001010=>2
11001011=>3
11001100=>4
11001101=>3
11001110=>2
11001111=>2
11010000=>3
11010001=>3
11010010=>3
11010011=>3
11010100=>4
11010101=>3
11010110=>2
11010111=>2
11011000=>2
11011001=>3
11011010=>2
11011011=>1
11011100=>2
11011101=>1
11011110=>1
11011111=>1
11100000=>3
11100001=>3
11100010=>3
11100011=>3
11100100=>2
11100101=>2
11100110=>3
11100111=>2
11101000=>4
11101001=>3
11101010=>3
11101011=>2
11101100=>2
11101101=>1
11101110=>1
11101111=>1
11110000=>4
11110001=>3
11110010=>2
11110011=>2
11110100=>3
11110101=>2
11110110=>1
11110111=>1
11111000=>3
11111001=>2
11111010=>2
11111011=>1
11111100=>2
11111101=>1
11111110=>1
11111111=>0
000000000=>0
000000001=>1
000000010=>1
000000011=>2
000000100=>1
000000101=>2
000000110=>2
000000111=>3
000001000=>1
000001001=>1
000001010=>2
000001011=>3
000001100=>2
000001101=>2
000001110=>3
000001111=>4
000010000=>1
000010001=>1
000010010=>1
000010011=>2
000010100=>2
000010101=>3
000010110=>3
000010111=>4
000011000=>2
000011001=>3
000011010=>2
000011011=>2
000011100=>3
000011101=>3
000011110=>4
000011111=>4
000100000=>1
000100001=>1
000100010=>1
000100011=>2
000100100=>1
000100101=>2
000100110=>3
000100111=>2
000101000=>2
000101001=>2
000101010=>3
000101011=>4
000101100=>3
000101101=>3
000101110=>4
000101111=>4
000110000=>2
000110001=>2
000110010=>3
000110011=>4
000110100=>3
000110101=>2
000110110=>2
000110111=>2
000111000=>3
000111001=>3
000111010=>3
000111011=>3
000111100=>3
000111101=>3
000111110=>3
000111111=>3
001000000=>1
001000001=>1
001000010=>1
001000011=>2
001000100=>1
001000101=>2
001000110=>2
001000111=>3
001001000=>1
001001001=>1
001001010=>2
001001011=>3
001001100=>3
001001101=>4
001001110=>2
001001111=>2
001010000=>2
001010001=>2
001010010=>2
001010011=>2
001010100=>3
001010101=>4
001010110=>4
001010111=>4
001011000=>3
001011001=>3
001011010=>3
001011011=>3
001011100=>3
001011101=>3
001011110=>3
001011111=>3
001100000=>2
001100001=>2
001100010=>2
001100011=>2
001100100=>3
001100101=>3
001100110=>4
001100111=>4
001101000=>3
001101001=>4
001101010=>3
001101011=>2
001101100=>2
001101101=>2
001101110=>2
001101111=>2
001110000=>3
001110001=>4
001110010=>2
001110011=>2
001110100=>3
001110101=>2
001110110=>2
001110111=>2
001111000=>3
001111001=>2
001111010=>2
001111011=>2
001111100=>2
001111101=>2
001111110=>2
001111111=>2
010000000=>1
010000001=>1
010000010=>1
010000011=>2
010000100=>1
010000101=>2
010000110=>2
010000111=>3
010001000=>1
010001001=>1
010001010=>2
010001011=>3
010001100=>2
010001101=>2
010001110=>4
010001111=>3
010010000=>1
010010001=>1
010010010=>1
010010011=>2
010010100=>2
010010101=>3
010010110=>4
010010111=>3
010011000=>3
010011001=>3
010011010=>4
010011011=>4
010011100=>2
010011101=>2
010011110=>2
010011111=>2
010100000=>2
010100001=>2
010100010=>2
010100011=>2
010100100=>2
010100101=>2
010100110=>3
010100111=>2
010101000=>3
010101001=>3
010101010=>4
010101011=>4
010101100=>3
010101101=>3
010101110=>3
010101111=>3
010110000=>2
010110001=>2
010110010=>4
010110011=>3
010110100=>3
010110101=>2
010110110=>2
010110111=>2
010111000=>3
010111001=>2
010111010=>2
010111011=>2
010111100=>2
010111101=>2
010111110=>2
010111111=>2
011000000=>2
011000001=>2
011000010=>2
011000011=>2
011000100=>2
011000101=>2
011000110=>2
011000111=>3
011001000=>3
011001001=>3
011001010=>3
011001011=>3
011001100=>4
011001101=>3
011001110=>3
011001111=>3
011010000=>3
011010001=>3
011010010=>4
011010011=>4
011010100=>4
011010101=>3
011010110=>2
011010111=>2
011011000=>2
011011001=>3
011011010=>2
011011011=>1
011011100=>2
011011101=>1
011011110=>1
011011111=>1
011100000=>3
011100001=>3
011100010=>4
011100011=>4
011100100=>2
011100101=>2
011100110=>3
011100111=>2
011101000=>4
011101001=>3
011101010=>3
011101011=>2
011101100=>2
011101101=>1
011101110=>1
011101111=>1
011110000=>4
011110001=>3
011110010=>2
011110011=>2
011110100=>3
011110101=>2
011110110=>1
011110111=>1
011111000=>3
011111001=>2
011111010=>2
011111011=>1
011111100=>2
011111101=>1
011111110=>1
011111111=>1
100000000=>1
100000001=>1
100000010=>1
100000011=>2
100000100=>1
100000101=>2
100000110=>2
100000111=>3
100001000=>1
100001001=>1
100001010=>2
100001011=>3
100001100=>2
100001101=>2
100001110=>3
100001111=>4
100010000=>1
100010001=>1
100010010=>1
100010011=>2
100010100=>2
100010101=>3
100010110=>3
100010111=>4
100011000=>2
100011001=>3
100011010=>2
100011011=>2
100011100=>4
100011101=>4
100011110=>3
100011111=>3
100100000=>1
100100001=>1
100100010=>1
100100011=>2
100100100=>1
100100101=>2
100100110=>3
100100111=>2
100101000=>2
100101001=>2
100101010=>3
100101011=>4
100101100=>4
100101101=>4
100101110=>3
100101111=>3
100110000=>3
100110001=>3
100110010=>3
100110011=>4
100110100=>3
100110101=>3
100110110=>3
100110111=>3
100111000=>3
100111001=>2
100111010=>2
100111011=>2
100111100=>2
100111101=>2
100111110=>2
100111111=>2
101000000=>2
101000001=>2
101000010=>2
101000011=>2
101000100=>2
101000101=>2
101000110=>2
101000111=>3
101001000=>2
101001001=>2
101001010=>2
101001011=>3
101001100=>3
101001101=>4
101001110=>2
101001111=>2
101010000=>3
101010001=>3
101010010=>3
101010011=>3
101010100=>4
101010101=>4
101010110=>3
101010111=>3
101011000=>2
101011001=>3
101011010=>2
101011011=>2
101011100=>2
101011101=>2
101011110=>2
101011111=>2
101100000=>2
101100001=>2
101100010=>2
101100011=>2
101100100=>4
101100101=>4
101100110=>3
101100111=>3
101101000=>3
101101001=>4
101101010=>3
101101011=>2
101101100=>2
101101101=>1
101101110=>1
101101111=>1
101110000=>3
101110001=>4
101110010=>2
101110011=>2
101110100=>3
101110101=>2
101110110=>1
101110111=>1
101111000=>3
101111001=>2
101111010=>2
101111011=>1
101111100=>2
101111101=>1
101111110=>1
101111111=>1
110000000=>2
110000001=>2
110000010=>2
110000011=>2
110000100=>2
110000101=>2
110000110=>2
110000111=>3
110001000=>2
110001001=>2
110001010=>2
110001011=>3
110001100=>2
110001101=>2
110001110=>4
110001111=>3
110010000=>2
110010001=>2
110010010=>2
110010011=>2
110010100=>2
110010101=>3
110010110=>4
110010111=>3
110011000=>4
110011001=>4
110011010=>3
110011011=>3
110011100=>2
110011101=>2
110011110=>2
110011111=>2
110100000=>3
110100001=>3
110100010=>3
110100011=>3
110100100=>3
110100101=>3
110100110=>3
110100111=>3
110101000=>4
110101001=>4
110101010=>4
110101011=>3
110101100=>2
110101101=>2
110101110=>2
110101111=>2
110110000=>2
110110001=>2
110110010=>4
110110011=>3
110110100=>3
110110101=>2
110110110=>1
110110111=>1
110111000=>3
110111001=>2
110111010=>2
110111011=>1
110111100=>2
110111101=>1
110111110=>1
110111111=>1
111000000=>3
111000001=>3
111000010=>3
111000011=>3
111000100=>3
111000101=>3
111000110=>3
111000111=>3
111001000=>2
111001001=>2
111001010=>2
111001011=>3
111001100=>4
111001101=>3
111001110=>2
111001111=>2
111010000=>4
111010001=>4
111010010=>3
111010011=>3
111010100=>4
111010101=>3
111010110=>2
111010111=>2
111011000=>2
111011001=>3
111011010=>2
111011011=>1
111011100=>2
111011101=>1
111011110=>1
111011111=>1
111100000=>4
111100001=>4
111100010=>3
111100011=>3
111100100=>2
111100101=>2
111100110=>3
111100111=>2
111101000=>4
111101001=>3
111101010=>3
111101011=>2
111101100=>2
111101101=>1
111101110=>1
111101111=>1
111110000=>4
111110001=>3
111110010=>2
111110011=>2
111110100=>3
111110101=>2
111110110=>1
111110111=>1
111111000=>3
111111001=>2
111111010=>2
111111011=>1
111111100=>2
111111101=>1
111111110=>1
111111111=>0
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
Description
Half the length of a longest factor which is its own reverse-complement of a binary word.
Code
def statistic(w): return max((l+1)//2 for a in range(len(w)) for l in range(len(w)-a) if all(w[a+i] == 1-w[a+l-i] for i in range(l)))
Created
Jun 12, 2019 at 07:02 by Martin Rubey
Updated
Jun 12, 2019 at 07:02 by Martin Rubey
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!