%I #15 Sep 08 2022 08:46:16

%S 6,24,61,136,249,364,481,600,721,844,969,1329,1684,2041,2400,2761,

%T 3124,3489,3856,4225,4596,4969,5344,5721,6100,6481,6864,7249,7636,

%U 8025,8416,8809,9204,9601,10249,11364,12481,13600,14721,15844,16969,18096

%N Numbers n such that the decimal number concat(3,n) is a square.

%C Elements are squares of integers in (sqrt(31), sqrt(40)) * sqrt(10)^k without the leading 3 elements for nonnegative k. - _David A. Corneth_, May 20 2016

%H Nathan Fox, <a href="/A273358/b273358.txt">Table of n, a(n) for n = 1..11067</a>

%e 61 is a member because 361 = 19^2 is a square.

%e 0 is not a member because 30 is not a square.

%p t1:=[];

%p for k from 1 to 20000 do

%p if issqr(k+3*10^length(k)) then t1:=[op(t1), k]; fi;

%p od;

%p t1;

%o (Magma) [n: n in [1..20000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(3)))]; // _Marius A. Burtea_, Mar 21 2019

%Y Cf. A272671, A273357, A273359, A273360, A273361, A273362, A273363, A273364.

%K nonn,base

%O 1,1

%A _Nathan Fox_, _Brooke Logan_, and _N. J. A. Sloane_, May 20 2016