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 A204099 #15 Jun 11 2014 09:08:21
%S A204099 0,3,3,9,9,15,9,27,3,27,9,27,9,3,27,9,27,9,27,33,69,9,27,57,45,27,15,
%T A204099 21,15,147,9,3,27,21,135,9,15,9,27,57,75,45,9,9,15,105,21,27,3,117,9,
%U A204099 45,27,21,63,81,3,51,15,45,27,51,3,21,15,9,93,27,39
%N A204099 Number of integers between successive twin prime pairs.
%C A204099 a(n) is divisible by 3.
%H A204099 Harvey P. Dale, <a href="/A204099/b204099.txt">Table of n, a(n) for n = 1..1000</a>
%F A204099 a(n) = A167132(n) - 1.
%F A204099 a(n) = A063091(n+1) - A063091(n) - 3.
%e A204099 a(1) = 0 because (3,5) is adjacent to (5,7); a(2) = 3 because the numbers 8, 9 and 10 are between (5,7) and (11,13), ...
%p A204099 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):od:
%t A204099 Module[{tr=Transpose[Select[Partition[Prime[Range[450]],2,1],#[[2]]- #[[1]] == 2&]],fir,las},fir=Rest[tr[[1]]];las=Most[tr[[2]]];Flatten[Abs[ Differences/@ Thread[{fir,las}]]]-1/.{-1->0}] (* _Harvey P. Dale_, Jun 11 2014 *)
%Y A204099 Cf. A046933, A063091, A167132, A204100.
%K A204099 nonn
%O A204099 1,2
%A A204099 _Michel Lagneau_, Jan 10 2012