cp's OEIS Frontend

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

%I A273364 #18 Sep 08 2022 08:46:16
%S A273364 61,216,409,604,801,1204,1809,2416,3025,3636,4249,4864,5481,6100,6721,
%T A273364 7344,7969,8596,9225,9856,10116,12025,13936,15849,17764,19681,21600,
%U A273364 23521,25444,27369,29296,31225,33156,35089,37024,38961,40900,42841,44784
%N A273364 Numbers n such that the decimal number concat(9,n) is a square.
%C A273364 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
%H A273364 Nathan Fox, <a href="/A273364/b273364.txt">Table of n, a(n) for n = 1..10000</a>
%e A273364 61 is a member because 961 = 31^2 is a square.
%e A273364 0 is not a member because 90 is not a square.
%p A273364 t1:=[];
%p A273364 for k from 1 to 50000 do
%p A273364 if issqr(k+9*10^length(k)) then t1:=[op(t1), k]; fi;
%p A273364 od;
%p A273364 t1;
%t A273364 Select[Range[45000],IntegerQ[Sqrt[9*10^IntegerLength[#]+#]]&] (* _Harvey P. Dale_, Feb 19 2020 *)
%o A273364 (Magma) [n: n in [1..50000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(9)))]; // _Vincenzo Librandi_, Feb 20 2020
%Y A273364 Cf. A272671, A273357, A273358, A273359, A273360, A273361, A273362, A273363.
%K A273364 nonn,base
%O A273364 1,1
%A A273364 _Nathan Fox_, _Brooke Logan_, and _N. J. A. Sloane_, May 20 2016