# Another Sequence Related To Binary Palindromes

franktaw at netscape.net franktaw at netscape.net
Wed Jul 16 00:28:47 CEST 2008

```Perhaps we should first ask, are there any other n for which a(n) > 1?
Looking
at the way the carries work when squaring a palindrome in binary, I
think not;
but I don't quite see how to prove it.

If the answer to this question is no, then this isn't a very
interesting sequence
-- it's just the characteristic sequence for binary palindromes, except
a(3) = 3

-----Original Message-----
From: Leroy Quet <q1qq2qqq3qqqq at yahoo.com>

I also just submitted this:

%S A000001 0,3,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,1
%N A000001 a(n) = the largest integer such that n^k is palindromic in
binary for
all nonnegative integers k that are <= a(n).
%C A000001 a(2n) = 0 for all n.
%e A000001 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.
%O A000001 2
%K A000001 ,more,nonn,

What are the n's where a(n) is a record?

Thanks,
Leroy Quet

```