A273363 Numbers m such that the decimal number concat(8,m) is a square.

1, 41, 100, 281, 464, 649, 836, 1225, 1796, 2369, 2944, 3521, 4100, 4681, 5264, 5849, 6436, 7025, 7616, 8209, 8804, 9401, 10000, 11801, 13604, 15409, 17216, 19025, 20836, 22649, 24464, 26281, 28100, 29921, 31744, 33569, 35396, 37225

Offset: 1

Author

Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016

Keywords

• nonn
• base

Comments

Elements are squares of integers in [9, sqrt(90)) * sqrt(10)^k without the leading 8 elements for nonnegative k. - David A. Corneth, May 20 2016

Examples

			41 is a member because 841 = 29^2 is a square.
0 is not a member because 80 is not a square.
		

Links

• Nathan Fox, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A272671, A273357, A273358, A273359, A273360, A273361, A273362, A273364.

Programs

Magma

[n: n in [1..20000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(8)))]; // Marius A. Burtea, Mar 21 2019

Maple

t1:=[];
for k from 1 to 50000 do
if issqr(k+8*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;

Mathematica

Select[Range[45000], IntegerQ[Sqrt[8 10^IntegerLength[#] + #]] &] (* Vincenzo Librandi, Feb 20 2020 *)

PARI

do(n)=my(v=List(),t); for(d=0,n, for(s=sqrtint(81*10^d-1)+1,sqrtint(90*10^d-1), listput(v,s^2-10^d*80))); Vec(v) \\ Charles R Greathouse IV, Nov 26 2016