A098036 First occurrence of primes p such that p = (prime(k) + prime(k+n))/2 for some positive integer k and n=2, 3, ...

5, 7, 11, 59, 11, 13, 41, 17, 23, 43, 23, 29, 53, 31, 67, 53, 37, 59, 41, 43, 97, 53, 103, 53, 79, 59, 83, 149, 67, 167, 71, 127, 89, 113, 83, 89, 101, 149, 311, 97, 101, 109, 101, 107, 113, 127, 137, 131, 157, 137, 127, 149, 137, 163, 137, 281, 193, 149, 229, 191, 157

Offset

2,1

Comments

No primes exist for n=1, as (prime(k) + prime(k+1))/2 is between prime(k) and prime(k+1) and so cannot be prime. See the Weisstein link.

Links

Table of n, a(n) for n=2..62.

Eric Weisstein's World of Mathematics, Interprime Numbers

Example

For n=2, (prime(2) + prime(2+2))/2 = (3+7)/2 = 5, so a(2)=5.
For n=4, (prime(2) + prime(2+4))/2 = (3+13)/2 = 8, which is not prime, but (prime(3) + prime(3+4))/2 = (5+17)/2 = 11, so a(4)=11.

Prog

(PARI) a(n) = {k=2; while(!isprime(p=(prime(k)+prime(k+n))/2), k++); p}

Crossrefs

Sequence in context: A106819 A045968 A066367 * A127269 A071781 A091509

Adjacent sequences: A098033 A098034 A098035 * A098037 A098038 A098039

Keyword

easy,nonn

Author

Cino Hilliard, Sep 10 2004

Extensions

Edited by Michael B. Porter, Oct 07 2009

Status

approved