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 A072570 #22 Jul 05 2018 11:05:08
%S A072570 4,6,12,18,30,42,60,72,102,108,120,138,144,150,180,186,192,198,228,
%T A072570 240,246,270,282,288,300,312,324,342,348,414,420,426,432,462,522,552,
%U A072570 570,582,600,618,636,642,660,696,714,780,792,810,816,822,828,834,846,858
%N A072570 Even interprimes i = (p+q)/2 (where p, q are consecutive primes) such that (q-p)/2 is not divisible by 3.
%C A072570 A superset of A014574. [_R. J. Mathar_, Mar 03 2009]
%H A072570 Harvey P. Dale, <a href="/A072570/b072570.txt">Table of n, a(n) for n = 1..1000</a>
%F A072570 If d = (P_{n+1} - P_n)/2 is even & d/2 == +/- 1 (mod 6), then P_n + d = (P_{n+1} + P_n)/2 is in the sequence. [Corrected by _M. F. Hasler_, Nov 29 2013]
%t A072570 a = Table[Prime[n], {n, 2, 200}]; b = {}; Do[d = (a[[n + 1]] - a[[n]])/2; If[ EvenQ[ a[[n]] + d] && (Mod[d, 6] == 5 || Mod[d, 6] == 1), b = Append[b, a[[n]] + d]], {n, 1, 198}]; b
%t A072570 Mean/@Select[Partition[Prime[Range[200]],2,1],EvenQ[Mean[#]] && !Divisible[ (#[[2]]-#[[1]])/2,3]&] (* _Harvey P. Dale_, Sep 27 2017 *)
%o A072570 (PARI) q=3;forprime(p=5,1e3,(s=q+q=p)%4==0 && (s-2*p)%3 && print1(s/2",")) \\ _M. F. Hasler_, Nov 29 2013
%o A072570 (PARI) is_A072570(n)=my(p=precprime(n));nextprime(n)+p==2*n && (n-p)%3 && !bittest(n,0) \\ _M. F. Hasler_, Nov 30 2013
%Y A072570 Cf. A024675, A072571. A072568 is union of A072571 and this sequence.
%K A072570 nonn
%O A072570 1,1
%A A072570 _Marco Matosic_, Jun 24 2002
%E A072570 Edited by _N. J. A. Sloane_ and _Robert G. Wilson v_, Jun 27 2002