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 A213997 #12 Jun 10 2014 11:56:14
%S A213997 0,0,17,53,0,77,29,77,29,107,173,173,29,17,203,179,17,119,47,0,113,
%T A213997 257,119,77,149,23,383,23,557,203,59,137,239,77,119,383,113,143,137,
%U A213997 29,257,239,17,143,539,623,1043,203,137,53,239,317,563,23,863,89,23,707
%N A213997 Number of integers between successive prime triples (p, p+2, p+6).
%C A213997 Property of this sequence: either a(n) is odd == 2 (mod 3), or a(n) =0.
%e A213997 a(3)= 17 because between the 3rd and 4th prime triples there are 17 integers: (17,19,23), 24, 25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40, (41,43,47).
%p A213997 A213997 := proc(n)
%p A213997 max(0,A022004(n+1)-A022004(n)-7) ;
%p A213997 end proc: # _R. J. Mathar_, Jul 11 2012
%t A213997 Flatten[Differences/@Table[Take[Flatten[Select[Partition[Prime[ Range[ 2000]],3,1], Differences[#]=={2,4}&]],{3n,3n+1}],{n,60}]]-1/.{-1->0} (* _Harvey P. Dale_, Jun 10 2014 *)
%Y A213997 Cf. A204099, A167132, A048614, A022004, A204100.
%K A213997 nonn
%O A213997 1,3
%A A213997 _Michel Lagneau_, Jun 30 2012