A140807 a(n) is the largest integer such that n^k is palindromic in binary for all nonnegative integers k that are <= a(n).

0, 3, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0

Offset

2,2

Comments

a(2n) = 0 for all n.

Links

Antti Karttunen, Table of n, a(n) for n = 2..65537

Formula

For n > 3, a(n)=0 or 1; moreover, a(n)=1 iff n belongs to A006995 (in other words, this sequence is an indicator function of A006995). - Max Alekseyev, Jul 22 2008

Example

The powers of 3 are, when written in binary: 1, 11, 1001, 11011, 1010001, ... Now, 3^k written in binary is palindromic for k = 0,1,2 and 3, but not for k=4. So a(3) = 3.

Mathematica

Array[If[EvenQ@ #, 0, Block[{k = 0}, While[PalindromeQ@ IntegerDigits[#^k, 2], k++]; k - 1]] &, 105, 2] (* Michael De Vlieger, Nov 13 2018 *)

Prog

(PARI) A140807(n) = for(k=1, oo, my(bs=binary(n^k)); if(Vecrev(bs)!=bs, return(k-1))); \\ Antti Karttunen, Nov 11 2018

Crossrefs

Cf. A006995.

Sequence in context: A317946 A347439 A347048 * A232629 A340007 A091959

Adjacent sequences: A140804 A140805 A140806 * A140808 A140809 A140810

Keyword

nonn,base

Author

Leroy Quet, Jul 15 2008

Extensions

More terms from Max Alekseyev, Jul 22 2008

Status

approved