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%I #34 Sep 08 2022 08:46:16
%S 6,21,44,69,96,156,225,296,369,444,521,600,681,764,849,936,1025,1236,
%T 1449,1664,1881,2100,2321,2544,2769,2996,3225,3456,3689,3924,4161,
%U 4400,4641,4884,5129,5376,5625,5876,6129,6384,6641,6900,7161,7424,7689,7956,8225,8496,8769,9044,9321,9600
%N Numbers k such that the decimal number 1k is a square.
%H Davin Park, <a href="/A272671/b272671.txt">Table of n, a(n) for n = 1..20000</a>
%e 44 is a member because 144 = 12^2 is a square.
%e 0 is not a member because 10 is not a square.
%p t1:=[];
%p for k from 1 to 20000 do
%p if issqr(k+10^length(k)) then t1:=[op(t1),k]; fi;
%p od;
%p t1;
%t Flatten[n /. Solve[10^# + n == a^2 && 10^(# - 1) <= n < 10^# && a > 0, {n, a}, Integers] & /@ Range[3]] (* _Davin Park_, Feb 05 2017 *)
%o (Magma) [n: n in [1..10000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(1)))]; // _Marius A. Burtea_, Mar 21 2019
%o (PARI) isok(n) = issquare(eval(concat(1, Str(n)))); \\ _Michel Marcus_, Mar 21 2019
%o (Python)
%o from sympy.ntheory.primetest import is_square
%o def ok(n): return is_square(int('1'+str(n)))
%o print(list(filter(ok, range(9601)))) # _Michael S. Branicky_, Jun 21 2021
%Y Cf. A265432, A272672, A045855 (squares beginning with 1), A272684, A272685.
%K nonn,base
%O 1,1
%A _Nathan Fox_, _Brooke Logan_, and _N. J. A. Sloane_, May 20 2016
%E Extended by _Davin Park_, Feb 05 2017
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