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 A285851 #26 May 16 2017 00:14:45
%S A285851 1,1,1,1,1,1,1,2,1,1,3,1,1,2,3,1,1,3,2,1,1,1,3,4,1,1,1,1,1,7,2,3,1,5,
%T A285851 1,3,1,2,3,3,1,5,1,1,1,3,6,1,1,2,3,1,5,1,3,1,1,3,2,1,5,7,1,1,2,7,3,5,
%U A285851 1,1,1,4,3,1,1,3,1,2,4,1,1,5,1,1,1,3,4,1,1,1,3,1,1,4,1,3,2,1,9,1,5,3,1,1,1,5
%N A285851 Denominator of the ratio of alternate consecutive prime gaps: Denominator((prime(n + 3) - prime(n + 2))/(prime(n + 1) - prime(n))).
%F A285851 a(n) = denominator((prime(n + 3) - prime(n + 2))/(prime(n + 1) - prime(n))).
%F A285851 A000040(n+3) = 5 + Sum_{k=1..n} ((1+(-1)^k)*Product_{j=1..k}(A286634(j)/a(j))^((1+(-1)^j)/2) + ((1-(-1)^k)/2)*Product_{j=1..k}(A286634(j)/a(j))^((1-(-1)^j)/2)), for n>0.
%F A285851 A001223(n+2) = (1+(-1)^n)*Product_{j=1..n}(A286634(j)/a(j))^((1+(-1)^j)/2) - ((-1+(-1)^n)/2)*Product_{j=1..n}(A286634(j)/a(j))^((1-(-1)^j)/2), for n>0.
%t A285851 Table[Denominator[(Prime[k+3]-Prime[k+2])/(Prime[k+1]-Prime[k])],{k,100}]
%Y A285851 Cf. A286634 (numerators), A001223, A000040, A274225, A276309.
%K A285851 nonn,frac
%O A285851 1,8
%A A285851 _Andres Cicuttin_, Apr 27 2017