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 A204100 #10 Jan 10 2016 14:52:56
%S A204100 0,1,1,3,3,5,3,9,1,9,3,9,3,1,9,3,9,3,9,11,23,3,9,19,15,9,5,7,5,49,3,1,
%T A204100 9,7,45,3,5,3,9,19,25,15,3,3,5,35,7,9,1,39,3,15,9,7,21,27,1,17,5,15,9,
%U A204100 17,1,7,5,3,31,9,13,9,13,55,13,21,9,7,5,19
%N A204100 Number of integers between successive twin primes, divided by 3.
%H A204100 Harvey P. Dale, <a href="/A204100/b204100.txt">Table of n, a(n) for n = 1..1000</a>
%F A204100 a(n) = (A063091(n+1)- A063091(n)-3)/3 = A204099(n)/3
%e A204100 a(2) = 1 because there exists three numbers 8, 9 and 10 between (5,7) and (11,13) => a(2) = 3/3 = 1.
%p A204100 T:=array(1..100,1..2):k:=0:for n from 1 to 1000 do:p1:=ithprime(n):p2:=ithprime(n+1):if p2-p1 = 2 then k:=k+1:T[k,1]:=p1:T[k,2]:=p2:else fi:od: for p from 2 to k do:x:= T[p+1,1]- T[p,2]: printf(`%d, `,(x-1)/3):od:
%t A204100 Join[{0},Rest[(#[[2]]-#[[1]]-1)/3&/@Partition[Rest[Flatten[Select[ Partition[ Prime[Range[500]],2,1],#[[2]]-#[[1]]==2&]]],2]]] (* _Harvey P. Dale_, Jan 10 2016 *)
%Y A204100 Cf. A028334, A063091, A046933, A204099.
%K A204100 nonn
%O A204100 1,4
%A A204100 _Michel Lagneau_, Jan 10 2012