A072570 -id:A072570 - 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

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

Original entry on oeis.org

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

Marco Matosic, Jun 24 2002

nonn

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

Cf. A024675, A072570. A072568 is union of A072570 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] == 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 *)

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

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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