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

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Sep 29 2008

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

PARI

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

Extensions

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