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

Author

Amarnath Murthy, Aug 15 2005

Keywords

• base
• easy
• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

Extensions

Corrected and extended by Joshua Zucker, May 04 2006

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