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 A094353 #20 Jun 17 2015 08:53:35
%S A094353 3,1,5,8,7,2,17,44,53,1011,7262969,27755899054,10713771825916682198,
%T A094353 1451983503000530523834049701901973110,
%U A094353 5317619734003376302895262678416297955761358855419919105266696681033714
%N A094353 Smallest integer not yet used such that 1 + Product_{k=1..n} a(k) is a square.
%C A094353 This sequence does not include every natural number. Suppose it contains b^2. Then letting A be the product up to b^2, we have A + 1 = i^2 and b^2 A + 1 = j^2. Multiplying the first equation by b^2 and subtracting, we get (bi)^2 = j^2 + b^2 - 1, which puts an upper bound on i and j (and hence on A). Probably the sequence contains no squares other than 1. - _Franklin T. Adams-Watters_, Aug 29 2006
%C A094353 a(n) <= 2 + Product_{k=1..n-1} a(k). - _Max Alekseyev_, Apr 26 2010
%e A094353 3 + 1 = 4, 3*1*5 + 1 = 16, 3*1*5*8 + 1 = 121 etc. are squares.
%o A094353 (PARI) v=[1];n=1;while(n<1100,s=1+n*prod(i=1,#v,v[i]);if(issquare(s)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ _Derek Orr_, Jun 16 2015
%Y A094353 Cf. A094354.
%K A094353 nonn
%O A094353 1,1
%A A094353 _Amarnath Murthy_, May 22 2004
%E A094353 More terms from _Franklin T. Adams-Watters_, Aug 29 2006
%E A094353 a(11) from _D. S. McNeil_, Mar 20 2009
%E A094353 a(12) from _Sean A. Irvine_, Nov 18 2009
%E A094353 a(13)-a(15) from _Max Alekseyev_, Apr 26 2010