Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001414
(load all 3 compositions to match this statistic)
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
St001414: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [2] => 10 => 0
1 => [1,1] => 11 => 0
00 => [3] => 100 => 0
01 => [2,1] => 101 => 1
10 => [1,2] => 110 => 0
11 => [1,1,1] => 111 => 1
000 => [4] => 1000 => 0
001 => [3,1] => 1001 => 0
010 => [2,2] => 1010 => 1
011 => [2,1,1] => 1011 => 1
100 => [1,3] => 1100 => 0
101 => [1,2,1] => 1101 => 0
110 => [1,1,2] => 1110 => 1
111 => [1,1,1,1] => 1111 => 1
0000 => [5] => 10000 => 0
0001 => [4,1] => 10001 => 2
0010 => [3,2] => 10010 => 0
0011 => [3,1,1] => 10011 => 0
0100 => [2,3] => 10100 => 1
0101 => [2,2,1] => 10101 => 2
0110 => [2,1,2] => 10110 => 1
0111 => [2,1,1,1] => 10111 => 1
1000 => [1,4] => 11000 => 0
1001 => [1,3,1] => 11001 => 0
1010 => [1,2,2] => 11010 => 0
1011 => [1,2,1,1] => 11011 => 2
1100 => [1,1,3] => 11100 => 1
1101 => [1,1,2,1] => 11101 => 1
1110 => [1,1,1,2] => 11110 => 1
1111 => [1,1,1,1,1] => 11111 => 2
00000 => [6] => 100000 => 0
00001 => [5,1] => 100001 => 0
00010 => [4,2] => 100010 => 2
00011 => [4,1,1] => 100011 => 2
00100 => [3,3] => 100100 => 0
00101 => [3,2,1] => 100101 => 0
00110 => [3,1,2] => 100110 => 0
00111 => [3,1,1,1] => 100111 => 0
01000 => [2,4] => 101000 => 1
01001 => [2,3,1] => 101001 => 1
01010 => [2,2,2] => 101010 => 2
01011 => [2,2,1,1] => 101011 => 2
01100 => [2,1,3] => 101100 => 1
01101 => [2,1,2,1] => 101101 => 1
01110 => [2,1,1,2] => 101110 => 1
01111 => [2,1,1,1,1] => 101111 => 1
10000 => [1,5] => 110000 => 0
10001 => [1,4,1] => 110001 => 0
10010 => [1,3,2] => 110010 => 0
10011 => [1,3,1,1] => 110011 => 0
Description
Half the length of the longest odd length palindromic prefix of a binary word. More precisely, this statistic is the largest number $k$ such that the word has a palindromic prefix of length $2k+1$.
Matching statistic: St001413
(load all 2 compositions to match this statistic)
Mapping
Mp00104: Binary words —reverse⟶ Binary words
Mp00269: Binary words —flag zeros to zeros⟶ Binary words
St001413: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 0 => 0
1 => 1 => 1 => 0
00 => 00 => 01 => 0
01 => 10 => 00 => 1
10 => 01 => 10 => 0
11 => 11 => 11 => 1
000 => 000 => 011 => 0
001 => 100 => 010 => 0
010 => 010 => 000 => 1
011 => 110 => 001 => 1
100 => 001 => 101 => 0
101 => 101 => 100 => 0
110 => 011 => 110 => 1
111 => 111 => 111 => 1
0000 => 0000 => 0111 => 0
0001 => 1000 => 0110 => 2
0010 => 0100 => 0100 => 0
0011 => 1100 => 0101 => 0
0100 => 0010 => 0001 => 1
0101 => 1010 => 0000 => 2
0110 => 0110 => 0010 => 1
0111 => 1110 => 0011 => 1
1000 => 0001 => 1011 => 0
1001 => 1001 => 1010 => 0
1010 => 0101 => 1000 => 0
1011 => 1101 => 1001 => 2
1100 => 0011 => 1101 => 1
1101 => 1011 => 1100 => 1
1110 => 0111 => 1110 => 1
1111 => 1111 => 1111 => 2
00000 => 00000 => 01111 => 0
00001 => 10000 => 01110 => 0
00010 => 01000 => 01100 => 2
00011 => 11000 => 01101 => 2
00100 => 00100 => 01001 => 0
00101 => 10100 => 01000 => 0
00110 => 01100 => 01010 => 0
00111 => 11100 => 01011 => 0
01000 => 00010 => 00011 => 1
01001 => 10010 => 00010 => 1
01010 => 01010 => 00000 => 2
01011 => 11010 => 00001 => 2
01100 => 00110 => 00101 => 1
01101 => 10110 => 00100 => 1
01110 => 01110 => 00110 => 1
01111 => 11110 => 00111 => 1
10000 => 00001 => 10111 => 0
10001 => 10001 => 10110 => 0
10010 => 01001 => 10100 => 0
10011 => 11001 => 10101 => 0
=> => => ? = 0
Description
Half the length of the longest even length palindromic prefix of a binary word.