A096269 a(n) = number of distinct palindromes of length n that occur in A096268.

2, 1, 3, 0, 4, 0, 3, 0, 4, 0, 4, 0, 3, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 3, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3

Offset: 1

Author

N. J. A. Sloane, Jun 22 2004

Keywords

• nonn
• easy
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• J.-P. Allouche, M. Baake, J. Cassaigns, and D. Damanik, Palindrome complexity, arXiv:math/0106121 [math.CO], 2001; Theoretical Computer Science, 292 (2003), 9-31.
• D. Damanik, Local symmetries in the period-doubling sequence, Discrete Appl. Math., 100 (2000), 115-121.

Crossrefs

Cf. A096268.

Programs

PARI

A096269(n) = if(n<=2,3-n,if(3==n,n,if(!(n%2),0,my(pp2=2^(#binary(n)-1)); if(((2*pp2)-n)<(n-pp2),3,4)))); \\ Antti Karttunen, Mar 30 2021

Formula

For even n >= 4, a(n) = 0; for odd n >= 5, a(n) = a(2n-1) = a(2n+1).

For odd n >= 5, let x be the power of 2 closest to n; if n > x then a(n) = 4 and if n < x then a(n) = 3. - David Wasserman, Nov 01 2007

Extensions

More terms from David Wasserman, Nov 01 2007