cp's OEIS Frontend

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

%I A273362 #17 Sep 08 2022 08:46:16
%S A273362 29,84,225,396,569,744,921,1289,1824,2361,2900,3441,3984,4529,5076,
%T A273362 5625,6176,6729,7284,7841,8400,8961,9524,10649,12336,14025,15716,
%U A273362 17409,19104,20801,22500,24201,25904,27609,29316,31025,32736,34449
%N A273362 Numbers n such that the decimal number concat(7,n) is a square.
%C A273362 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
%H A273362 Nathan Fox, <a href="/A273362/b273362.txt">Table of n, a(n) for n = 1..10000</a>
%e A273362 84 is a member because 784 = 28^2 is a square.
%e A273362 0 is not a member because 70 is not a square.
%p A273362 t1:=[];
%p A273362 for k from 1 to 50000 do
%p A273362 if issqr(k+7*10^length(k)) then t1:=[op(t1), k]; fi;
%p A273362 od;
%p A273362 t1;
%t A273362 Select[Range[35000],IntegerQ[Sqrt[7*10^IntegerLength[#]+#]]&] (* _Harvey P. Dale_, Feb 10 2019 *)
%o A273362 (Magma) [n: n in [1..20000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(7)))]; // _Marius A. Burtea_, Mar 21 2019
%Y A273362 Cf. A272671, A273357, A273358, A273359, A273360, A273361, A273363, A273364.
%K A273362 nonn,base
%O A273362 1,1
%A A273362 _Nathan Fox_, _Brooke Logan_, and _N. J. A. Sloane_, May 20 2016