A273362 Numbers n such that the decimal number concat(7,n) is a square.

29, 84, 225, 396, 569, 744, 921, 1289, 1824, 2361, 2900, 3441, 3984, 4529, 5076, 5625, 6176, 6729, 7284, 7841, 8400, 8961, 9524, 10649, 12336, 14025, 15716, 17409, 19104, 20801, 22500, 24201, 25904, 27609, 29316, 31025, 32736, 34449

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(71), sqrt(80)) * sqrt(10)^k without the leading 7 elements for nonnegative k. - David A. Corneth, May 20 2016

Examples

			84 is a member because 784 = 28^2 is a square.
0 is not a member because 70 is not a square.
		

Links

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

Crossrefs

Cf. A272671, A273357, A273358, A273359, A273360, A273361, A273363, A273364.

Programs

Magma

[n: n in [1..20000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(7)))]; // Marius A. Burtea, Mar 21 2019

Maple

t1:=[];
for k from 1 to 50000 do
if issqr(k+7*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;

Mathematica

Select[Range[35000],IntegerQ[Sqrt[7*10^IntegerLength[#]+#]]&] (* Harvey P. Dale, Feb 10 2019 *)