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

1,1

Comments

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A063932, A063933.

Sequence in context: A140297 A234853 A060863 * A326643 A222030 A327261

Adjacent sequences: A063931 A063932 A063933 * A063935 A063936 A063937

Keyword

nonn

Author

Henry Bottomley, Aug 21 2001

Status

approved