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 A191996 #9 Mar 30 2012 18:49:34 %S A191996 2,3,45,175,693,11011,2807805,302307005,402243205,714186915, %T A191996 42803602439,11086133031701,5908908905896633,1488200914442251997, %U A191996 3041106216468949733,16213234917387714257,21611220383343195817,77778782159652161745383,67745319261057032880228593 %N A191996 Numerators of partial products of a Hardy-Littlewood constant. %C A191996 The rational partial products are r(n)=a(n)/A191997(n), n>=1. %C A191996 The limit r(n), n->infinity, approximately 1.3203236 = A114907, is the constant C(f_1,f_2) appearing in the Hardy-Littlewood conjecture (also called Bateman-Horn conjecture) for the integer polynomials f_1=x and f_2=x+2 (relevant for twin primes). See the Conrad reference Example 1, p. 134, also for the original references. %C A191996 Essentially the same as A062270. - R. J. Mathar, Jun 23 2011 %D A191996 Keith Conrad, Hardy-Littlewood constants, pp. 133-154 in: Mathematical properties of sequences and other combinatorial structures, edts. Jong-Seon No et al., Kluwer, Boston/Dordrecht/London, 2003. %H A191996 Wolfdieter Lang, <a href="/A191996/a191996.txt">Rationals and limit.</a> %F A191996 a(n) = numerator(r(n)), with the rational r(n):=2*product(1-1/(p(j)-1)^2,j=2..n), with the primes p(j):=A000040(j). %e A191996 The rationals r(n) (in lowest terms) are 2, 3/2, 45/32, 175/128, 693/512, 11011/8192,... %Y A191996 A191997, A191998/A191999. %K A191996 nonn,easy,frac %O A191996 2,1 %A A191996 _Wolfdieter Lang_, Jun 21 2011