- FindStat

Identifier

St001413: Binary words ⟶ ℤ

Values

0 => 0

1 => 0

00 => 1

01 => 0

10 => 0

11 => 1

000 => 1

001 => 1

010 => 0

011 => 0

100 => 0

101 => 0

110 => 1

111 => 1

0000 => 2

0001 => 1

0010 => 1

0011 => 1

0100 => 0

0101 => 0

0110 => 2

0111 => 0

1000 => 0

1001 => 2

1010 => 0

1011 => 0

1100 => 1

1101 => 1

1110 => 1

1111 => 2

00000 => 2

00001 => 2

00010 => 1

00011 => 1

00100 => 1

00101 => 1

00110 => 1

00111 => 1

01000 => 0

01001 => 0

01010 => 0

01011 => 0

01100 => 2

01101 => 2

01110 => 0

01111 => 0

10000 => 0

10001 => 0

10010 => 2

10011 => 2

10100 => 0

10101 => 0

10110 => 0

10111 => 0

11000 => 1

11001 => 1

11010 => 1

11011 => 1

11100 => 1

11101 => 1

11110 => 2

11111 => 2

000000 => 3

000001 => 2

000010 => 2

000011 => 2

000100 => 1

000101 => 1

000110 => 1

000111 => 1

001000 => 1

001001 => 1

001010 => 1

001011 => 1

001100 => 3

001101 => 1

001110 => 1

001111 => 1

010000 => 0

010001 => 0

010010 => 3

010011 => 0

010100 => 0

010101 => 0

010110 => 0

010111 => 0

011000 => 2

011001 => 2

011010 => 2

011011 => 2

011100 => 0

011101 => 0

011110 => 3

011111 => 0

100000 => 0

100001 => 3

100010 => 0

100011 => 0

100100 => 2

100101 => 2

100110 => 2

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Description

Half the length of the longest even length 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//2 for k in range(0,len(w)+1,2) if w[:k] == w[:k][::-1])

Created

Jun 11, 2019 at 07:24 by Martin Rubey

Updated

Mar 05, 2020 at 13:41 by Martin Rubey