A072571 Even interprimes i = (p+q)/2 (where p, q are consecutive primes) such that (q-p)/2 is divisible by 3.

26, 34, 50, 56, 64, 76, 86, 134, 154, 160, 170, 176, 236, 254, 260, 266, 274, 334, 356, 370, 376, 386, 436, 446, 506, 532, 544, 560, 566, 574, 590, 596, 604, 610, 650, 656, 680, 730, 736, 754, 944, 950, 974, 980, 994, 1016, 1036, 1066, 1078, 1100, 1106

Offset: 1

Author

Marco Matosic, Jun 24 2002

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A024675, A072570. A072568 is union of A072570 and this sequence.

Programs

Mathematica

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
Select[Mean/@Select[Partition[Prime[Range[200]],2,1],Divisible[(#[[2]]- #[[1]])/ 2,3]&],EvenQ] (* Harvey P. Dale, May 09 2021 *)

Formula

(P_n+1 - P_n)/2 is even but not divisible by 4.

Extensions

Edited by N. J. A. Sloane and Robert G. Wilson v, Jun 27 2002