A023114 Squares that remain square when the digit 9 is appended.
0, 4, 16, 324, 6400, 23716, 467856, 9229444, 34199104, 674648676, 13308852496, 49315084900, 972842923584, 19191356070436, 71112318227344, 1402838821160100, 27673922144716864, 102543913568745796, 2022892607269941264
Offset: 1
Programs
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Mathematica
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 *)
Formula
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
Comments