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

1,2

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Sequence in context: A220444 A355799 A117678 * A262753 A055851 A025494

Adjacent sequences: A167042 A167043 A167044 * A167046 A167047 A167048

Keyword

nonn,base

Author

Claudio Meller, Oct 27 2009

Extensions

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

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

Status

approved