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

1,1

Links

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A133635 A167705 A061673 * A307033 A058763 A291158

Adjacent sequences: A072568 A072569 A072570 * A072572 A072573 A072574

Keyword

nonn

Author

Marco Matosic, Jun 24 2002

Extensions

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

Status

approved