%I
%S 0,1,14641,104060401,1004006004001,10004000600040001,
%T 100004000060000400001,1000004000006000004000001,
%U 10000004000000600000040000001,100000004000000060000000400000001
%N Fourth powers that are palindromic in base 10.
%C See A056810 (the main entry for this problem) for further information, including the search limit.  _N. J. A. Sloane_, Mar 07 2011.
%C Conjecture: If k^4 is a palindrome > 0, then k begins and ends with digit 1, all other digits of k being 0.
%C The number of zeros in 1x1, where the x are zeros, is the same as (the number of zeros)/4 in (1x1)^4 = 1x4x6x4x1.
%H P. De Geest, <a href="http://users.skynet.be/worldofnumbers/cube.htm">Palindromic cubes</a> (The Simmons test is mentioned here)
%H G. J. Simmons, <a href="/A002778/a002778_2.pdf">Palindromic powers</a>, J. Rec. Math., 3 (No. 2, 1970), 9398. [Annotated scanned copy]
%F a(n) = A056810(n)^4
%t Do[If[Module[{idn = IntegerDigits[n^4, 10]}, idn == Reverse[idn]], Print[n^4]], {n, 100000001}]
%o (MAGMA) [ p: n in [0..10000000]  s eq Reverse(s) where s is Intseq(p) where p is n^4 ];
%Y Cf. A002113, A168576, A056810, A002778, A002779.
%K nonn,base
%O 1,3
%A _Matevz Markovic_, Feb 11 2011
