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A186080 Fourth powers that are palindromic in base 10. 2


%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), 93-98. [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

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