A167045 Squares that remains a square when some single digit is inserted in front of its decimal expansion.

1, 4, 9, 25, 100, 225, 400, 625, 900, 1225, 2025, 2500, 3025, 4225, 5625, 7225, 10000, 22500, 30625, 40000, 50625, 62500, 70225, 75625, 90000, 93025, 122500, 202500, 250000, 302500, 330625, 422500, 455625, 562500, 722500, 765625, 950625, 1000000

Offset: 1

Author

Claudio Meller, Oct 27 2009

Keywords

• nonn
• base

Examples

			225 is in the sequence because both 225 and 1225 are squares.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000

Programs

Maple

a := proc (n) local s, c, j: s := proc (n) options operator, arrow: nops(convert(n, base, 10)) end proc: c := 0: for j to 9 do if type(sqrt(j*10^s(n^2)+n^2), integer) = true then c := c+1 else end if end do: if 0 < c then n^2 else end if end proc: seq(a(n), n = 1 .. 1200); # Emeric Deutsch, Nov 01 2009

Mathematica

srsQ[n_]:=AnyTrue[Range[9]*10^IntegerLength[n]+n,IntegerQ[Sqrt[#]]&]; Select[ Range[1200]^2,srsQ] (* The program uses the AnyTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 19 2016 *)

Formula

Union of A167035, A167036, A167037, A167038, A167039, A167041, A167042, A167043 and A167044. [R. J. Mathar, Oct 30 2009]

Extensions

Edited by N. J. A. Sloane, Oct 29 2009

More terms from R. J. Mathar and Emeric Deutsch, Oct 30 2009