Identifier
- St001415: Binary words ⟶ ℤ
Values
=>
0=>1
1=>1
00=>2
01=>1
10=>1
11=>2
000=>3
001=>2
010=>3
011=>1
100=>1
101=>3
110=>2
111=>3
0000=>4
0001=>3
0010=>2
0011=>2
0100=>3
0101=>3
0110=>4
0111=>1
1000=>1
1001=>4
1010=>3
1011=>3
1100=>2
1101=>2
1110=>3
1111=>4
00000=>5
00001=>4
00010=>3
00011=>3
00100=>5
00101=>2
00110=>2
00111=>2
01000=>3
01001=>3
01010=>5
01011=>3
01100=>4
01101=>4
01110=>5
01111=>1
10000=>1
10001=>5
10010=>4
10011=>4
10100=>3
10101=>5
10110=>3
10111=>3
11000=>2
11001=>2
11010=>2
11011=>5
11100=>3
11101=>3
11110=>4
11111=>5
000000=>6
000001=>5
000010=>4
000011=>4
000100=>3
000101=>3
000110=>3
000111=>3
001000=>5
001001=>5
001010=>2
001011=>2
001100=>6
001101=>2
001110=>2
001111=>2
010000=>3
010001=>3
010010=>6
010011=>3
010100=>5
010101=>5
010110=>3
010111=>3
011000=>4
011001=>4
011010=>4
011011=>4
011100=>5
011101=>5
011110=>6
011111=>1
100000=>1
100001=>6
100010=>5
100011=>5
100100=>4
100101=>4
100110=>4
100111=>4
101000=>3
101001=>3
101010=>5
101011=>5
101100=>3
101101=>6
101110=>3
101111=>3
110000=>2
110001=>2
110010=>2
110011=>6
110100=>2
110101=>2
110110=>5
110111=>5
111000=>3
111001=>3
111010=>3
111011=>3
111100=>4
111101=>4
111110=>5
111111=>6
0000000=>7
0000001=>6
0000010=>5
0000011=>5
0000100=>4
0000101=>4
0000110=>4
0000111=>4
0001000=>7
0001001=>3
0001010=>3
0001011=>3
0001100=>3
0001101=>3
0001110=>3
0001111=>3
0010000=>5
0010001=>5
0010010=>5
0010011=>5
0010100=>7
0010101=>2
0010110=>2
0010111=>2
0011000=>6
0011001=>6
0011010=>2
0011011=>2
0011100=>7
0011101=>2
0011110=>2
0011111=>2
0100000=>3
0100001=>3
0100010=>7
0100011=>3
0100100=>6
0100101=>6
0100110=>3
0100111=>3
0101000=>5
0101001=>5
0101010=>7
0101011=>5
0101100=>3
0101101=>3
0101110=>3
0101111=>3
0110000=>4
0110001=>4
0110010=>4
0110011=>4
0110100=>4
0110101=>4
0110110=>7
0110111=>4
0111000=>5
0111001=>5
0111010=>5
0111011=>5
0111100=>6
0111101=>6
0111110=>7
0111111=>1
1000000=>1
1000001=>7
1000010=>6
1000011=>6
1000100=>5
1000101=>5
1000110=>5
1000111=>5
1001000=>4
1001001=>7
1001010=>4
1001011=>4
1001100=>4
1001101=>4
1001110=>4
1001111=>4
1010000=>3
1010001=>3
1010010=>3
1010011=>3
1010100=>5
1010101=>7
1010110=>5
1010111=>5
1011000=>3
1011001=>3
1011010=>6
1011011=>6
1011100=>3
1011101=>7
1011110=>3
1011111=>3
1100000=>2
1100001=>2
1100010=>2
1100011=>7
1100100=>2
1100101=>2
1100110=>6
1100111=>6
1101000=>2
1101001=>2
1101010=>2
1101011=>7
1101100=>5
1101101=>5
1101110=>5
1101111=>5
1110000=>3
1110001=>3
1110010=>3
1110011=>3
1110100=>3
1110101=>3
1110110=>3
1110111=>7
1111000=>4
1111001=>4
1111010=>4
1111011=>4
1111100=>5
1111101=>5
1111110=>6
1111111=>7
00000000=>8
00000001=>7
00000010=>6
00000011=>6
00000100=>5
00000101=>5
00000110=>5
00000111=>5
00001000=>4
00001001=>4
00001010=>4
00001011=>4
00001100=>4
00001101=>4
00001110=>4
00001111=>4
00010000=>7
00010001=>7
00010010=>3
00010011=>3
00010100=>3
00010101=>3
00010110=>3
00010111=>3
00011000=>8
00011001=>3
00011010=>3
00011011=>3
00011100=>3
00011101=>3
00011110=>3
00011111=>3
00100000=>5
00100001=>5
00100010=>5
00100011=>5
00100100=>8
00100101=>5
00100110=>5
00100111=>5
00101000=>7
00101001=>7
00101010=>2
00101011=>2
00101100=>2
00101101=>2
00101110=>2
00101111=>2
00110000=>6
00110001=>6
00110010=>6
00110011=>6
00110100=>2
00110101=>2
00110110=>2
00110111=>2
00111000=>7
00111001=>7
00111010=>2
00111011=>2
00111100=>8
00111101=>2
00111110=>2
00111111=>2
01000000=>3
01000001=>3
01000010=>8
01000011=>3
01000100=>7
01000101=>7
01000110=>3
01000111=>3
01001000=>6
01001001=>6
01001010=>6
01001011=>6
01001100=>3
01001101=>3
01001110=>3
01001111=>3
01010000=>5
01010001=>5
01010010=>5
01010011=>5
01010100=>7
01010101=>7
01010110=>5
01010111=>5
01011000=>3
01011001=>3
01011010=>8
01011011=>3
01011100=>3
01011101=>3
01011110=>3
01011111=>3
01100000=>4
01100001=>4
01100010=>4
01100011=>4
01100100=>4
01100101=>4
01100110=>8
01100111=>4
01101000=>4
01101001=>4
01101010=>4
01101011=>4
01101100=>7
01101101=>7
01101110=>4
01101111=>4
01110000=>5
01110001=>5
01110010=>5
01110011=>5
01110100=>5
01110101=>5
01110110=>5
01110111=>5
01111000=>6
01111001=>6
01111010=>6
01111011=>6
01111100=>7
01111101=>7
01111110=>8
01111111=>1
10000000=>1
10000001=>8
10000010=>7
10000011=>7
10000100=>6
10000101=>6
10000110=>6
10000111=>6
10001000=>5
10001001=>5
10001010=>5
10001011=>5
10001100=>5
10001101=>5
10001110=>5
10001111=>5
10010000=>4
10010001=>4
10010010=>7
10010011=>7
10010100=>4
10010101=>4
10010110=>4
10010111=>4
10011000=>4
10011001=>8
10011010=>4
10011011=>4
10011100=>4
10011101=>4
10011110=>4
10011111=>4
10100000=>3
10100001=>3
10100010=>3
10100011=>3
10100100=>3
10100101=>8
10100110=>3
10100111=>3
10101000=>5
10101001=>5
10101010=>7
10101011=>7
10101100=>5
10101101=>5
10101110=>5
10101111=>5
10110000=>3
10110001=>3
10110010=>3
10110011=>3
10110100=>6
10110101=>6
10110110=>6
10110111=>6
10111000=>3
10111001=>3
10111010=>7
10111011=>7
10111100=>3
10111101=>8
10111110=>3
10111111=>3
11000000=>2
11000001=>2
11000010=>2
11000011=>8
11000100=>2
11000101=>2
11000110=>7
11000111=>7
11001000=>2
11001001=>2
11001010=>2
11001011=>2
11001100=>6
11001101=>6
11001110=>6
11001111=>6
11010000=>2
11010001=>2
11010010=>2
11010011=>2
11010100=>2
11010101=>2
11010110=>7
11010111=>7
11011000=>5
11011001=>5
11011010=>5
11011011=>8
11011100=>5
11011101=>5
11011110=>5
11011111=>5
11100000=>3
11100001=>3
11100010=>3
11100011=>3
11100100=>3
11100101=>3
11100110=>3
11100111=>8
11101000=>3
11101001=>3
11101010=>3
11101011=>3
11101100=>3
11101101=>3
11101110=>7
11101111=>7
11110000=>4
11110001=>4
11110010=>4
11110011=>4
11110100=>4
11110101=>4
11110110=>4
11110111=>4
11111000=>5
11111001=>5
11111010=>5
11111011=>5
11111100=>6
11111101=>6
11111110=>7
11111111=>8
000000000=>9
000000001=>8
000000010=>7
000000011=>7
000000100=>6
000000101=>6
000000110=>6
000000111=>6
000001000=>5
000001001=>5
000001010=>5
000001011=>5
000001100=>5
000001101=>5
000001110=>5
000001111=>5
000010000=>9
000010001=>4
000010010=>4
000010011=>4
000010100=>4
000010101=>4
000010110=>4
000010111=>4
000011000=>4
000011001=>4
000011010=>4
000011011=>4
000011100=>4
000011101=>4
000011110=>4
000011111=>4
000100000=>7
000100001=>7
000100010=>7
000100011=>7
000100100=>3
000100101=>3
000100110=>3
000100111=>3
000101000=>9
000101001=>3
000101010=>3
000101011=>3
000101100=>3
000101101=>3
000101110=>3
000101111=>3
000110000=>8
000110001=>8
000110010=>3
000110011=>3
000110100=>3
000110101=>3
000110110=>3
000110111=>3
000111000=>9
000111001=>3
000111010=>3
000111011=>3
000111100=>3
000111101=>3
000111110=>3
000111111=>3
001000000=>5
001000001=>5
001000010=>5
001000011=>5
001000100=>9
001000101=>5
001000110=>5
001000111=>5
001001000=>8
001001001=>8
001001010=>5
001001011=>5
001001100=>5
001001101=>5
001001110=>5
001001111=>5
001010000=>7
001010001=>7
001010010=>7
001010011=>7
001010100=>9
001010101=>2
001010110=>2
001010111=>2
001011000=>2
001011001=>2
001011010=>2
001011011=>2
001011100=>2
001011101=>2
001011110=>2
001011111=>2
001100000=>6
001100001=>6
001100010=>6
001100011=>6
001100100=>6
001100101=>6
001100110=>6
001100111=>6
001101000=>2
001101001=>2
001101010=>2
001101011=>2
001101100=>9
001101101=>2
001101110=>2
001101111=>2
001110000=>7
001110001=>7
001110010=>7
001110011=>7
001110100=>2
001110101=>2
001110110=>2
001110111=>2
001111000=>8
001111001=>8
001111010=>2
001111011=>2
001111100=>9
001111101=>2
001111110=>2
001111111=>2
010000000=>3
010000001=>3
010000010=>9
010000011=>3
010000100=>8
010000101=>8
010000110=>3
010000111=>3
010001000=>7
010001001=>7
010001010=>7
010001011=>7
010001100=>3
010001101=>3
010001110=>3
010001111=>3
010010000=>6
010010001=>6
010010010=>9
010010011=>6
010010100=>6
010010101=>6
010010110=>6
010010111=>6
010011000=>3
010011001=>3
010011010=>3
010011011=>3
010011100=>3
010011101=>3
010011110=>3
010011111=>3
010100000=>5
010100001=>5
010100010=>5
010100011=>5
010100100=>5
010100101=>5
010100110=>5
010100111=>5
010101000=>7
010101001=>7
010101010=>9
010101011=>7
010101100=>5
010101101=>5
010101110=>5
010101111=>5
010110000=>3
010110001=>3
010110010=>3
010110011=>3
010110100=>8
010110101=>8
010110110=>3
010110111=>3
010111000=>3
010111001=>3
010111010=>9
010111011=>3
010111100=>3
010111101=>3
010111110=>3
010111111=>3
011000000=>4
011000001=>4
011000010=>4
011000011=>4
011000100=>4
011000101=>4
011000110=>9
011000111=>4
011001000=>4
011001001=>4
011001010=>4
011001011=>4
011001100=>8
011001101=>8
011001110=>4
011001111=>4
011010000=>4
011010001=>4
011010010=>4
011010011=>4
011010100=>4
011010101=>4
011010110=>9
011010111=>4
011011000=>7
011011001=>7
011011010=>7
011011011=>7
011011100=>4
011011101=>4
011011110=>4
011011111=>4
011100000=>5
011100001=>5
011100010=>5
011100011=>5
011100100=>5
011100101=>5
011100110=>5
011100111=>5
011101000=>5
011101001=>5
011101010=>5
011101011=>5
011101100=>5
011101101=>5
011101110=>9
011101111=>5
011110000=>6
011110001=>6
011110010=>6
011110011=>6
011110100=>6
011110101=>6
011110110=>6
011110111=>6
011111000=>7
011111001=>7
011111010=>7
011111011=>7
011111100=>8
011111101=>8
011111110=>9
011111111=>1
100000000=>1
100000001=>9
100000010=>8
100000011=>8
100000100=>7
100000101=>7
100000110=>7
100000111=>7
100001000=>6
100001001=>6
100001010=>6
100001011=>6
100001100=>6
100001101=>6
100001110=>6
100001111=>6
100010000=>5
100010001=>9
100010010=>5
100010011=>5
100010100=>5
100010101=>5
100010110=>5
100010111=>5
100011000=>5
100011001=>5
100011010=>5
100011011=>5
100011100=>5
100011101=>5
100011110=>5
100011111=>5
100100000=>4
100100001=>4
100100010=>4
100100011=>4
100100100=>7
100100101=>7
100100110=>7
100100111=>7
100101000=>4
100101001=>9
100101010=>4
100101011=>4
100101100=>4
100101101=>4
100101110=>4
100101111=>4
100110000=>4
100110001=>4
100110010=>8
100110011=>8
100110100=>4
100110101=>4
100110110=>4
100110111=>4
100111000=>4
100111001=>9
100111010=>4
100111011=>4
100111100=>4
100111101=>4
100111110=>4
100111111=>4
101000000=>3
101000001=>3
101000010=>3
101000011=>3
101000100=>3
101000101=>9
101000110=>3
101000111=>3
101001000=>3
101001001=>3
101001010=>8
101001011=>8
101001100=>3
101001101=>3
101001110=>3
101001111=>3
101010000=>5
101010001=>5
101010010=>5
101010011=>5
101010100=>7
101010101=>9
101010110=>7
101010111=>7
101011000=>5
101011001=>5
101011010=>5
101011011=>5
101011100=>5
101011101=>5
101011110=>5
101011111=>5
101100000=>3
101100001=>3
101100010=>3
101100011=>3
101100100=>3
101100101=>3
101100110=>3
101100111=>3
101101000=>6
101101001=>6
101101010=>6
101101011=>6
101101100=>6
101101101=>9
101101110=>6
101101111=>6
101110000=>3
101110001=>3
101110010=>3
101110011=>3
101110100=>7
101110101=>7
101110110=>7
101110111=>7
101111000=>3
101111001=>3
101111010=>8
101111011=>8
101111100=>3
101111101=>9
101111110=>3
101111111=>3
110000000=>2
110000001=>2
110000010=>2
110000011=>9
110000100=>2
110000101=>2
110000110=>8
110000111=>8
110001000=>2
110001001=>2
110001010=>2
110001011=>2
110001100=>7
110001101=>7
110001110=>7
110001111=>7
110010000=>2
110010001=>2
110010010=>2
110010011=>9
110010100=>2
110010101=>2
110010110=>2
110010111=>2
110011000=>6
110011001=>6
110011010=>6
110011011=>6
110011100=>6
110011101=>6
110011110=>6
110011111=>6
110100000=>2
110100001=>2
110100010=>2
110100011=>2
110100100=>2
110100101=>2
110100110=>2
110100111=>2
110101000=>2
110101001=>2
110101010=>2
110101011=>9
110101100=>7
110101101=>7
110101110=>7
110101111=>7
110110000=>5
110110001=>5
110110010=>5
110110011=>5
110110100=>5
110110101=>5
110110110=>8
110110111=>8
110111000=>5
110111001=>5
110111010=>5
110111011=>9
110111100=>5
110111101=>5
110111110=>5
110111111=>5
111000000=>3
111000001=>3
111000010=>3
111000011=>3
111000100=>3
111000101=>3
111000110=>3
111000111=>9
111001000=>3
111001001=>3
111001010=>3
111001011=>3
111001100=>3
111001101=>3
111001110=>8
111001111=>8
111010000=>3
111010001=>3
111010010=>3
111010011=>3
111010100=>3
111010101=>3
111010110=>3
111010111=>9
111011000=>3
111011001=>3
111011010=>3
111011011=>3
111011100=>7
111011101=>7
111011110=>7
111011111=>7
111100000=>4
111100001=>4
111100010=>4
111100011=>4
111100100=>4
111100101=>4
111100110=>4
111100111=>4
111101000=>4
111101001=>4
111101010=>4
111101011=>4
111101100=>4
111101101=>4
111101110=>4
111101111=>9
111110000=>5
111110001=>5
111110010=>5
111110011=>5
111110100=>5
111110101=>5
111110110=>5
111110111=>5
111111000=>6
111111001=>6
111111010=>6
111111011=>6
111111100=>7
111111101=>7
111111110=>8
111111111=>9
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
The length of the longest palindromic prefix of a binary word.
References
[1] Gabric, D., Shallit, J. Borders, Palindrome Prefixes, and Square Prefixes arXiv:1906.03689
Code
def statistic(w): return max(k for k in range(len(w)+1) if w[:k] == w[:k][::-1])
Created
Jun 11, 2019 at 07:18 by Martin Rubey
Updated
Mar 05, 2020 at 14:09 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!