%I #11 May 09 2021 11:10:28
%S 26,34,50,56,64,76,86,134,154,160,170,176,236,254,260,266,274,334,356,
%T 370,376,386,436,446,506,532,544,560,566,574,590,596,604,610,650,656,
%U 680,730,736,754,944,950,974,980,994,1016,1036,1066,1078,1100,1106
%N Even interprimes i = (p+q)/2 (where p, q are consecutive primes) such that (q-p)/2 is divisible by 3.
%H Amiram Eldar, <a href="/A072571/b072571.txt">Table of n, a(n) for n = 1..10000</a>
%F (P_n+1 - P_n)/2 is even but not divisible by 4.
%t a = Table[Prime[n], {n, 2, 200}]; b = {}; Do[d = (a[[n + 1]] - a[[n]])/2; If[ EvenQ[ a[[n]] + d] && Mod[d, 6] == 3, b = Append[b, a[[n]] + d]], {n, 1, 198}]; b
%t Select[Mean/@Select[Partition[Prime[Range[200]],2,1],Divisible[(#[[2]]- #[[1]])/ 2,3]&],EvenQ] (* _Harvey P. Dale_, May 09 2021 *)
%Y Cf. A024675, A072570. A072568 is union of A072570 and this sequence.
%K nonn
%O 1,1
%A _Marco Matosic_, Jun 24 2002
%E Edited by _N. J. A. Sloane_ and _Robert G. Wilson v_, Jun 27 2002