- FindStat

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

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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