login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072570 Even interprimes i = (p+q)/2 (where p, q are consecutive primes) such that (q-p)/2 is not divisible by 3. 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 (list; graph; refs; listen; history; text; internal format)
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: A074998 A061715 A280469 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 03:20 EST 2019. Contains 329383 sequences. (Running on oeis4.)