This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A265432 #59 Apr 12 2017 23:48:24
%S A265432 225,6,1025,6,225,9937257544619140625,80625,225,19025,14797831640625,
%T A265432 5625,89450791534674072265625,96,69,44,21,1993672119140625,
%U A265432 2002541101386962890625,225,6,8734765625,99758030615478515625,5625,863225,80625,6,40625,225,890625,158764150390625
%N A265432 a(n) = smallest k with concat(1,k) and concat(n,k) both square numbers.
%C A265432 k must be a positive integer (and of course cannot begin with 0). - _N. J. A. Sloane_, May 19 2016
%C A265432 Every term is a member of A272671, by definition. Certainly every term of A272671 which is a power of 100 times an earlier term of A272671 (such as 600, 2100, 4400) will not appear, by the "smallest k" condition. Does every other term of A272671 (that is, the terms of A272684) eventually appear? See A272685 and A273369 for the first appearance of these terms. - _Nathan Fox_, _Brooke Logan_, and _N. J. A. Sloane_, May 23 2016
%H A265432 N. J. A. Sloane, <a href="/A265432/b265432.txt">Table of n, a(n) for n = 0..20000</a>, May 25 2016 [First 10000 terms from David W. Wilson, Dec 08 2015]
%H A265432 N. J. A. Sloane, <a href="/A265432/a265432.txt">Table of n, a(n), sqrt(concat(n,a(n))), sqrt(concat(1,a(n)))</a> (based on _David W. Wilson_ 10000-term b-file)
%H A265432 David W. Wilson, <a href="/A265432/a265432_1.txt">Table of n, a(n) for n = 0..10000</a>, May 25 2016 [The graph of the first 10000 terms looks rather different from the graph of the first 20000 terms, so this file is worth preserving. - _N. J. A. Sloane_, May 25 2016]
%e A265432 a(0) = 225 because 1225 is a square as is (0)225. (In other words, 225 is the first term in A272672 that is itself a square). - _N. J. A. Sloane_, May 21 2016
%e A265432 a(2) = 1025 because concat(1,1025) = 11025 = 105^2 and concat(2,1025) = 21025 = 145^2.
%t A265432 << Combinatorica`
%t A265432 A265432[0] = 225;
%t A265432 A265432[1] = 6;
%t A265432 A265432[n_] := Block[{x = {-1, 1, 0, 1}[[Mod[n, 4, 1]]], d = Infinity, l, i}, While[d > Sqrt[10.0^(x - 1)] (Sqrt[10.0 n + 1] - Sqrt[11.0]), x++; d = Infinity; l = Divisors[((n - 1) 10^x)/4]; i = BinarySearch[l, 0.5 Sqrt[(n + 1) 10.0^x - 1] - 0.5 Sqrt[2*10.0^x - 1]]; If[i <= Length@l, d = 2*l[[i + 1/2]]]]; (((n - 1) 10^x - d^2)/(2 d))^2 - 10^x] (* _Davin Park_, Apr 11 2017 *)
%Y A265432 Cf. A045855, A272671, A018796, A272684, A272685 and A273369 (smallest inverse).
%Y A265432 For records see A272674, A272675.
%Y A265432 For square roots referred to in definition see A272682, A272683.
%Y A265432 A018851 is a simpler sequence in the same spirit.
%K A265432 nonn,base,look
%O A265432 0,1
%A A265432 _David W. Wilson_ and _Robert G. Wilson v_, Dec 08 2015