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

Author

Marco Matosic, Jun 24 2002

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A024675, A072571. A072568 is union of A072571 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] == 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 *)

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

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]

Extensions

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