A110811 Perfect powers not a multiple of 10 whose digit reversal is also a perfect power (not necessarily with the same exponent, but with exponent > 1).

1, 4, 8, 9, 121, 144, 169, 343, 441, 484, 676, 961, 1089, 1331, 9801, 10201, 10404, 10609, 12321, 12544, 12769, 14641, 14884, 40401, 40804, 44521, 44944, 48841, 69696, 90601, 94249, 96721, 698896, 1002001, 1004004, 1006009, 1022121, 1024144

Offset

1,2

Comments

All palindromic perfect powers are trivial members, but there are infinitely many nontrivial members.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..867

Example

12^2 =144, digit reversal of 144 is 441= 21^2. 12769=113^2, reversal(12769) = 96721 = 311^2.

Mathematica

Join[{1}, Select[Range[11 10^5], Mod[#, 10]!=0&&GCD@@FactorInteger[#][[All, 2]]>1&&GCD@@FactorInteger[IntegerReverse[#]][[All, 2]]>1&]] (* Harvey P. Dale, Jun 01 2018 *)

Crossrefs

This is a subset of A115656 and also a subset of A001597. See also A118895 to include terms with trailing zeros.

Sequence in context: A217700 A118895 A327654 * A226035 A128827 A075786

Adjacent sequences: A110808 A110809 A110810 * A110812 A110813 A110814

Keyword

base,easy,nonn

Author

Amarnath Murthy, Aug 15 2005

Extensions

Corrected and extended by Joshua Zucker, May 04 2006

Description and offset edited by Chai Wah Wu, Jun 06 2016

Status

approved