A273364 Numbers n such that the decimal number concat(9,n) is a square.

61, 216, 409, 604, 801, 1204, 1809, 2416, 3025, 3636, 4249, 4864, 5481, 6100, 6721, 7344, 7969, 8596, 9225, 9856, 10116, 12025, 13936, 15849, 17764, 19681, 21600, 23521, 25444, 27369, 29296, 31225, 33156, 35089, 37024, 38961, 40900, 42841, 44784

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 (sqrt(91), 10) * sqrt(10)^k without the leading 9 elements for nonnegative k. - David A. Corneth, May 20 2016

Examples

			61 is a member because 961 = 31^2 is a square.
0 is not a member because 90 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, A273363.

Programs

Magma

[n: n in [1..50000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(9)))]; // Vincenzo Librandi, Feb 20 2020

Maple

t1:=[];
for k from 1 to 50000 do
if issqr(k+9*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;

Mathematica

Select[Range[45000],IntegerQ[Sqrt[9*10^IntegerLength[#]+#]]&] (* Harvey P. Dale, Feb 19 2020 *)