A072571 -id:A072571 - cp's OEIS frontend

A072568 Even interprimes.

4, 6, 12, 18, 26, 30, 34, 42, 50, 56, 60, 64, 72, 76, 86, 102, 108, 120, 134, 138, 144, 150, 154, 160, 170, 176, 180, 186, 192, 198, 228, 236, 240, 246, 254, 260, 266, 270, 274, 282, 288, 300, 312, 324, 334, 342, 348, 356, 370, 376, 386, 414, 420, 426, 432

Offset: 1

Marco Matosic, Jun 21 2002

The interprimes (A024675) are those integers that lie at the midpoint between consecutive odd primes.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Interprime

Even members of A024675.

Cf. A024675, A072569, A072570, A072571, A072572, A072573.

Select[Plus @@@ Partition[Table[Prime[n], {n, 2, 100}], 2, 1]/2, EvenQ]

Offset corrected by Amiram Eldar, Mar 23 2020

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

Original entry on oeis.org

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

Marco Matosic, Jun 24 2002

nonn

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

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

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

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 *)

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

is_A072570(n)=my(p=precprime(n));nextprime(n)+p==2*n && (n-p)%3 && !bittest(n,0) \\ M. F. Hasler, Nov 30 2013

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]

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

cp's OEIS Frontend

A072568 Even interprimes.

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