A072570 Even interprimes i = (p+q)/2 (where p, q are consecutive primes) such that (q-p)/2 is not divisible by 3.

4, 6, 12, 18, 30, 42, 60, 72, 102, 108, 120, 138, 144, 150, 180, 186, 192, 198, 228, 240, 246, 270, 282, 288, 300, 312, 324, 342, 348, 414, 420, 426, 432, 462, 522, 552, 570, 582, 600, 618, 636, 642, 660, 696, 714, 780, 792, 810, 816, 822, 828, 834, 846, 858

Offset

1,1

Comments

A superset of A014574. [R. J. Mathar, Mar 03 2009]

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

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]

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] == 5 || Mod[d, 6] == 1), b = Append[b, a[[n]] + d]], {n, 1, 198}]; b
Mean/@Select[Partition[Prime[Range[200]], 2, 1], EvenQ[Mean[#]] && !Divisible[ (#[[2]]-#[[1]])/2, 3]&] (* Harvey P. Dale, Sep 27 2017 *)

Prog

(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
(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

Crossrefs

Cf. A024675, A072571. A072568 is union of A072571 and this sequence.

Sequence in context: A061715 A280469 A353073 * A217259 A014574 A258838

Adjacent sequences: A072567 A072568 A072569 * A072571 A072572 A072573

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