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A186080 Fourth powers that are palindromic in base 10. 2
0, 1, 14641, 104060401, 1004006004001, 10004000600040001, 100004000060000400001, 1000004000006000004000001, 10000004000000600000040000001, 100000004000000060000000400000001 (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..10.

P. De Geest, Palindromic cubes (The Simmons test is mentioned here)

G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [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 A256839 A015312

Adjacent sequences:  A186077 A186078 A186079 * A186081 A186082 A186083

KEYWORD

nonn,base

AUTHOR

Matevz Markovic, Feb 11 2011

STATUS

approved

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Last modified December 5 03:30 EST 2016. Contains 278755 sequences.