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 A091852 #15 Jul 21 2015 00:26:42
%S A091852 2,19,208,3023,52004,1079263,24845332,663589691,21809669044,
%T A091852 769910292199,31595368408378,1432693760237483,67842962092519574,
%U A091852 3469898586979325623,198354535000733806154,12566530264688830748431
%N A091852 Numerator of Sum_{i=1..n} prime(i)/prime(i+1).
%C A091852 Proposed by Mohammed BOUAYOUN, Feb 16 2004; computed by _R. K. Guy_, Feb 17 2004
%e A091852 The sums are f(1)=2/3, f(2)=2/3 + 3/5, f(3)=2/3+3/5+5/7, f(4)=2/3+3/5+5/7+7/11, ...
%t A091852 A091852[n_] := Numerator[ Sum[ Prime[i] / Prime[i + 1], {i, n}]]; Table[ A091852[n], {n, 16}] (* _Robert G. Wilson v_, Mar 16 2004 *)
%Y A091852 Denominators are in A070826.
%K A091852 nonn,frac
%O A091852 1,1
%A A091852 _N. J. A. Sloane_, Mar 13 2004
%E A091852 More terms from _Robert G. Wilson v_, Mar 16 2004