A113800 Numbers k such that k^2 plus the reverse of k^2 gives a perfect power.

2, 231, 1010, 102010, 451429, 1000100, 9426681, 1000001000, 8803095102, 10002000100, 56017891104, 1000000010000, 4811618419542

Offset: 1

Author

Giovanni Resta, Jan 22 2006

Keywords

• base
• nonn
• more

Comments

Sequence is infinite since it contains all the numbers of the form (1+100^k)*10^k and (1+100^k)^2*10^k, for k >= 1. - Giovanni Resta, Sep 24 2013

Examples

			451429^2 = 203788142041 and 203788142041 + 140241887302 = 7007^3,
9426681^2 = 88862314675761 and 88862314675761 + 16757641326888 = 10277157^2.
		

Crossrefs

Cf. A000290, A002942, A061226.

Programs

Mathematica

ppQ[n_] := n != 1 && GCD @@ (Transpose[FactorInteger[n]][[2]]) > 1; rev[n_] := FromDigits@Reverse@IntegerDigits@n ; lst = {}; Do[If[ppQ[n^2 + rev[n^2]], AppendTo[lst, n]], {n, 10^6}]; lst

Extensions

a(8)-a(13) from Giovanni Resta, Sep 24 2013