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

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), 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

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