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A140807
a(n) is the largest integer such that n^k is palindromic in binary for all nonnegative integers k that are <= a(n).
1
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
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: A347439 A347048 A374213 * A232629 A340007 A091959
KEYWORD
nonn,base
AUTHOR
Leroy Quet, Jul 15 2008
EXTENSIONS
More terms from Max Alekseyev, Jul 22 2008
STATUS
approved