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 A082462 #3 Mar 30 2012 17:38:50
%S A082462 0,1,2,2,3,3,4,4,4,5,5,5,6,6,6,6,7,7,7,8,8,8,8,8,8,9,9,10,10,10,10,10,
%T A082462 11,11,12,12,12,12,12,12,13,13,14,14,15,15,15,15,16,16,16,17,17,17,17,
%U A082462 17,18,18,18,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21
%N A082462 Let chi(k) = 1 if prime(k+1) - prime(k) = 2, = 0 otherwise; sequence gives a(n) = sum_{k <= n} chi(k).
%F A082462 a(n)=A071538(A000040(n)). [From _R. J. Mathar_, Oct 06 2008]
%e A082462 n p D a(n) (p=prime(n), D = prime(n+1)-prime(n))
%e A082462 1 2 1 0
%e A082462 2 3 2 1
%e A082462 3 5 2 2
%e A082462 4 7 4 2
%e A082462 5 11 2 3
%e A082462 6 13 4 3
%Y A082462 Cf. A000040, A001223.
%K A082462 nonn
%O A082462 1,3
%A A082462 Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Apr 26 2003