A023112 -id:A023112 - cp's OEIS frontend

A023113 Squares that remain square when the digit 6 is appended.

1, 25, 1849, 36481, 2666689, 52606009, 3845364121, 75857828929, 5545012396225, 109386936710041, 7995904029992761, 157735886878050625, 11530088066237165569, 227455039491212291641, 16626378995609962758169

Offset: 1

David W. Wilson

The terms of the sequence are the squares of the y-values in the solution to the Pellian equation x^2-10*y^2=6. - Colin Barker, Sep 28 2013

Cf. A023111, A023112, A023114.

Empirical g.f.: -x*(x^4+24*x^3+382*x^2+24*x+1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)). - Colin Barker, Jan 31 2013

Definition modified by Harvey P. Dale, Sep 08 2019

A023114 Squares that remain square when the digit 9 is appended.

Original entry on oeis.org

0, 4, 16, 324, 6400, 23716, 467856, 9229444, 34199104, 674648676, 13308852496, 49315084900, 972842923584, 19191356070436, 71112318227344, 1402838821160100, 27673922144716864, 102543913568745796, 2022892607269941264

Offset: 1

David W. Wilson

The terms of the sequence are the squares of the y-values in the solution to the Pellian equation x^2-10*y^2=9. - Colin Barker, Sep 28 2013

Cf. A023111, A023112, A023113.

Select[Range[0,10^6]^2,IntegerQ[Sqrt[10#+9]]&] (* The program generates the first 13 terms of the sequence. *) (* Harvey P. Dale, Jul 21 2024 *)

Empirical g.f.: -4*x^2*(x+1)*(x^4+2*x^3+75*x^2+2*x+1) / ((x-1)*(x^6-1442*x^3+1)). - Colin Barker, Jan 31 2013

cp's OEIS Frontend

A023113 Squares that remain square when the digit 6 is appended.

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