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

1,1

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

Links

Table of n, a(n) for n=1..13.

Example

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

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

Crossrefs

Cf. A000290, A002942, A061226.

Sequence in context: A015968 A286447 A095220 * A133495 A066622 A261493

Adjacent sequences: A113797 A113798 A113799 * A113801 A113802 A113803

Keyword

base,nonn,more

Author

Giovanni Resta, Jan 22 2006

Extensions

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

Status

approved