A063934 Numbers which are either prime or the average of consecutive odd primes.

2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 23, 26, 29, 30, 31, 34, 37, 39, 41, 42, 43, 45, 47, 50, 53, 56, 59, 60, 61, 64, 67, 69, 71, 72, 73, 76, 79, 81, 83, 86, 89, 93, 97, 99, 101, 102, 103, 105, 107, 108, 109, 111, 113, 120, 127, 129, 131, 134, 137, 138

Offset: 1

Author

Henry Bottomley, Aug 21 2001

Keywords

• nonn

Comments

Numbers n such that nextprime(n-1) + prevprime(n+1) = 2n. - Wesley Ivan Hurt, May 13 2017

Examples

			7 is prime, 9 is the average of 7 and 11, 11 is prime, 12 is the average of 11 and 13; so 7, 9, 11 and 13 are in the sequence.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A063932, A063933.

Programs

Mathematica

Function[p, Union@ Join[p, Rest@ Map[Mean, Partition[p, 2, 1]]]]@ Prime@ Range@ 34 (* Michael De Vlieger, May 13 2017 *)

PARI

{ for (n=1, 1000, if (n==1, a=2; p=3, if (n%2, a=(q + p=nextprime(q + 1))/2, a=q=p)); write("b063934.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 03 2009

Formula

For n >= 1: a(2n)=A000040(n+1); a(2n+1)=(A000040(n+1)+A000040(n+2))/2 =A024675(n).