

A186080


Fourth powers that are palindromic in base 10.


4



0, 1, 14641, 104060401, 1004006004001, 10004000600040001, 100004000060000400001, 1000004000006000004000001, 10000004000000600000040000001, 100000004000000060000000400000001, 1000000004000000006000000004000000001, 10000000004000000000600000000040000000001, 100000000004000000000060000000000400000000001
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

See A056810 (the main entry for this problem) for further information, including the search limit.  N. J. A. Sloane, Mar 07 2011.
Conjecture: If k^4 is a palindrome > 0, then k begins and ends with digit 1, all other digits of k being 0.
The number of zeros in 1x1, where the x are zeros, is the same as (the number of zeros)/4 in (1x1)^4 = 1x4x6x4x1.


LINKS

Table of n, a(n) for n=1..13.
P. De Geest, Palindromic cubes (The Simmons test is mentioned here) [broken link]
G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 9398. [Annotated scanned copy]


FORMULA

a(n) = A056810(n)^4.


MATHEMATICA

Do[If[Module[{idn = IntegerDigits[n^4, 10]}, idn == Reverse[idn]], Print[n^4]], {n, 100000001}]


PROG

(Magma) [ p: n in [0..10000000]  s eq Reverse(s) where s is Intseq(p) where p is n^4 ];


CROSSREFS

Cf. A002113, A168576, A056810, A002778, A002779.
Sequence in context: A017284 A017392 A017656 * A013861 A291145 A256839
Adjacent sequences: A186077 A186078 A186079 * A186081 A186082 A186083


KEYWORD

nonn,base


AUTHOR

Matevz Markovic, Feb 11 2011


EXTENSIONS

a(11)a(13) using extensions of A056810 from Hugo Pfoertner, Oct 22 2021


STATUS

approved



