# [seqfan] Re: Which palindromes are fourth powers?

APPLEGATE, DAVID L (DAVID L) david at research.att.com
Sat Oct 24 02:14:59 CEST 2015

```Err, sorry, I misread the sequence.  Ignore that remark.
-Dave

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of APPLEGATE, DAVID L (DAVID L)
Sent: Friday, October 23, 2015 7:55 PM
To: 'Sequence Fanatics Discussion list'
Subject: [seqfan] Re: Which palindromes are fourth powers?

> The sequence contains no term with digit sum 3. - Vladimir Shevelev, May 23 2011
is true for all squares, and hence all fourth powers, and hence this sequence, because digit sum 3 implies divisible by 3, but divisible by 9 would imply digit sum divisible by 9.
-Dave

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil Sloane
Sent: Friday, October 23, 2015 6:58 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Which palindromes are fourth powers?

Dear Sequence Fans, A056810 gives numbers n such that n^4 is a palindrome.
The initial terms were calculated by Bob Wilson, back in the year 2000.
They are
0, 1, 11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001 The question is, is every term of the form 10^k+1?
It would be nice to have some more terms - or some theorems.
There is a claim that:

The sequence contains no term with digit sum 3. - Vladimir Shevelev, May 23
2011

but I don't know if this claim (which seems very plausible) has been checked.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.