cp's OEIS Frontend

A273363 Numbers m such that the decimal number concat(8,m) is a square.

%I A273363 #22 Sep 08 2022 08:46:16
%S A273363 1,41,100,281,464,649,836,1225,1796,2369,2944,3521,4100,4681,5264,
%T A273363 5849,6436,7025,7616,8209,8804,9401,10000,11801,13604,15409,17216,
%U A273363 19025,20836,22649,24464,26281,28100,29921,31744,33569,35396,37225
%N A273363 Numbers m such that the decimal number concat(8,m) is a square.
%C A273363 Elements are squares of integers in [9, sqrt(90)) * sqrt(10)^k without the leading 8 elements for nonnegative k. - _David A. Corneth_, May 20 2016
%H A273363 Nathan Fox, <a href="/A273363/b273363.txt">Table of n, a(n) for n = 1..10000</a>
%e A273363 41 is a member because 841 = 29^2 is a square.
%e A273363 0 is not a member because 80 is not a square.
%p A273363 t1:=[];
%p A273363 for k from 1 to 50000 do
%p A273363 if issqr(k+8*10^length(k)) then t1:=[op(t1), k]; fi;
%p A273363 od;
%p A273363 t1;
%t A273363 Select[Range[45000], IntegerQ[Sqrt[8 10^IntegerLength[#] + #]] &] (* _Vincenzo Librandi_, Feb 20 2020 *)
%o A273363 (PARI) do(n)=my(v=List(),t); for(d=0,n, for(s=sqrtint(81*10^d-1)+1,sqrtint(90*10^d-1), listput(v,s^2-10^d*80))); Vec(v) \\ _Charles R Greathouse IV_, Nov 26 2016
%o A273363 (Magma) [n: n in [1..20000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(8)))]; // _Marius A. Burtea_, Mar 21 2019
%Y A273363 Cf. A272671, A273357, A273358, A273359, A273360, A273361, A273362, A273364.
%K A273363 nonn,base
%O A273363 1,2
%A A273363 _Nathan Fox_, _Brooke Logan_, and _N. J. A. Sloane_, May 20 2016