cp's OEIS Frontend

A273360 Numbers n such that the decimal number concat(5,n) is a square.

%I A273360 #17 Sep 08 2022 08:46:16
%S A273360 29,76,184,329,476,625,776,929,1076,1529,1984,2441,2900,3361,3824,
%T A273360 4289,4756,5225,5696,6169,6644,7121,7600,8081,8564,9049,9536,11225,
%U A273360 12656,14089,15524,16961,18400,19841,21284,22729,24176,25625,27076
%N A273360 Numbers n such that the decimal number concat(5,n) is a square.
%C A273360 Elements are squares of integers in (sqrt(51), sqrt(60)) * sqrt(10)^k without the leading 5 elements for nonnegative k. - _David A. Corneth_, May 20 2016
%H A273360 Nathan Fox, <a href="/A273360/b273360.txt">Table of n, a(n) for n = 1..10000</a>
%e A273360 76 is a member because 576 = 24^2 is a square.
%e A273360 0 is not a member because 50 is not a square.
%p A273360 t1:=[];
%p A273360 for k from 1 to 50000 do
%p A273360 if issqr(k+5*10^length(k)) then t1:=[op(t1), k]; fi;
%p A273360 od;
%p A273360 t1;
%t A273360 Select[Range[30000],IntegerQ[Sqrt[5*10^IntegerLength[#]+#]]&] (* _Harvey P. Dale_, Jan 01 2019 *)
%o A273360 (Magma) [n: n in [1..10000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(5)))]; // _Marius A. Burtea_, Mar 21 2019
%Y A273360 Cf. A272671, A273357, A273358, A273359, A273361, A273362, A273363, A273364.
%K A273360 nonn,base
%O A273360 1,1
%A A273360 _Nathan Fox_, _Brooke Logan_, and _N. J. A. Sloane_, May 20 2016