cp's OEIS Frontend

A115549 Numbers k such that the concatenation of k with 8*k gives a square.

%I A115549 #20 Apr 13 2022 13:02:13
%S A115549 3,12,28,63,112,278,1112,2778,11112,27778,111112,277778,1111112,
%T A115549 2777778,4938272,7716050,11111112,12802888,13151250,13504288,13862002,
%U A115549 14224392,14591458,14963200,15339618,15720712,16106482,16496928,16892050,17291848,17696322,18105472
%N A115549 Numbers k such that the concatenation of k with 8*k gives a square.
%C A115549 If k = 10*R_m + 2, with m >= 1, then the concatenation of k with 8*k equals (30*R_m + 6)^2, so A047855 \ {1,2} is a subsequence. - _Bernard Schott_, Apr 09 2022
%C A115549 Numbers k such that A009470(k) is a square. - _Michel Marcus_, Apr 09 2022
%C A115549 The numbers 28, 278, 2778, ..., 2*10^k + 7*(10^k - 1)/9 + 1, ..., k >= 1, are terms, because the concatenation forms the squares 28224 = 168^2, 2782224 = 1668^2, 277822224 = 16668^2, ..., (10^m + 2*(10^m - 1)/3 + 2)^2, m >= 2, ... - _Marius A. Burtea_, Apr 10 2022
%H A115549 Marius A. Burtea, <a href="/A115549/b115549.txt">Table of n, a(n) for n = 1..176</a>
%e A115549 3_24 = 18^2.
%e A115549 11112_88896 = 33336^2.
%o A115549 (PARI) isok(k) = issquare(eval(Str(k, 8*k))); \\ _Michel Marcus_, Apr 09 2022
%o A115549 (Magma) [n:n in [1..20000000]|IsSquare(Seqint(Intseq(8*n) cat Intseq(n)))]; // _Marius A. Burtea_, Apr 10 2022
%Y A115549 Cf. A002275, A047855, A009470, A102567, A106497, A115527-A115556.
%K A115549 nonn,base
%O A115549 1,1
%A A115549 _Giovanni Resta_, Jan 25 2006
%E A115549 More terms from _Marius A. Burtea_, Apr 13 2022