A145025 - OEIS

A145025

Numbers which are the average of two consecutive odd primes (A024675) together with primes which are the average of the previous prime and the following prime (A006562).

4, 5, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 53, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, 102, 105, 108, 111, 120, 129, 134, 138, 144, 150, 154, 157, 160, 165, 170, 173, 176, 180, 186, 192, 195, 198, 205, 211, 217, 225, 228, 231, 236, 240, 246, 254, 257, 260

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Numbers n such that prevprime(n) + nextprime(n) = 2n. - Wesley Ivan Hurt, May 13 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

Primes:= select(isprime, [seq(i, i=3..1000, 2)]):

nprimes:= nops(Primes):

A024675:= {seq((Primes[i]+Primes[i+1])/2, i=1..nprimes-1)}:

L:= Primes[1..-3]+Primes[3..-1]:

A006562:=zip((s, t) -> if 2*s=t then s else NULL fi, Primes[2..-2], L):

sort(convert(convert(A006562, set) union A024675, list)); # Robert Israel, Nov 20 2016

MATHEMATICA

Union[Select[Map[Mean@ {First@ #, Last@ #} &, Partition[#, 3, 1]], PrimeQ], Map[Mean, Partition[#, 2, 1]]] &@ Prime@ Range[2, 56] (* Michael De Vlieger, Jan 31 2019 *)

PROG

(PARI) for(n=2, 999, n-precprime(n-1)==nextprime(n+1)-n&&print1(n", ")) \\ M. F. Hasler, Jun 01 2013

CROSSREFS

Equals A024675 U A006562. - M. F. Hasler, Jun 01 2013

Sequence in context: A003156 A192360 A115984 * A245236 A209122 A073263

Adjacent sequences: A145022 A145023 A145024 * A145026 A145027 A145028

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Sep 29 2008

EXTENSIONS

Entry revised by N. J. A. Sloane, Mar 24 2017, replacing old definition with definition from M. F. Hasler

STATUS

approved