This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A186080 #66 Aug 11 2024 14:41:34
%S A186080 0,1,14641,104060401,1004006004001,10004000600040001,
%T A186080 100004000060000400001,1000004000006000004000001,
%U A186080 10000004000000600000040000001,100000004000000060000000400000001,1000000004000000006000000004000000001,10000000004000000000600000000040000000001,100000000004000000000060000000000400000000001
%N A186080 Fourth powers that are palindromic in base 10.
%C A186080 See A056810 (the main entry for this problem) for further information, including the search limit. - _N. J. A. Sloane_, Mar 07 2011
%C A186080 Conjecture: If k^4 is a palindrome > 0, then k begins and ends with digit 1, all other digits of k being 0.
%C A186080 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 A186080 P. De Geest, <a href="https://users.skynet.be/worldofnumbers/cube.htm">Palindromic cubes</a> (The Simmons test is mentioned here) [broken link]
%H A186080 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 A186080 a(n) = A056810(n)^4.
%t A186080 Do[If[Module[{idn = IntegerDigits[n^4, 10]}, idn == Reverse[idn]], Print[n^4]], {n, 100000001}]
%o A186080 (Magma) [ p: n in [0..10000000] | s eq Reverse(s) where s is Intseq(p) where p is n^4 ];
%Y A186080 Cf. A002113, A168576, A056810, A002778, A002779.
%K A186080 nonn,base
%O A186080 1,3
%A A186080 _Matevz Markovic_, Feb 11 2011
%E A186080 a(11)-a(13) using extensions of A056810 from _Hugo Pfoertner_, Oct 22 2021