A092940 a(n) = largest prime p such that 2*prime(n) - p is prime.

2, 3, 7, 11, 19, 23, 31, 31, 43, 53, 59, 71, 79, 83, 89, 103, 113, 109, 131, 139, 139, 151, 163, 173, 191, 199, 199, 211, 211, 223, 251, 257, 271, 271, 293, 283, 311, 313, 331, 317, 353, 359, 379, 383, 389, 379, 419, 443, 449, 439, 463, 467, 479, 499, 509, 523

Offset: 1

Author

Amarnath Murthy, Mar 23 2004

Keywords

• nonn

Comments

a(n) = largest prime p such that prime(n) = (p+q)/2, where q is also prime.

prime(n) <= a(n) < 2*prime(n).

Conjecture: a(n) = prime(n) only for n = 1 and 2.

Examples

			2*prime(18) = 122; the primes smaller than 122 are 113, 109, 107, ... in descending order. 122 - 113 = 9 is not prime, but 122 - 109 = 13 is prime, hence a(18) = 109.
		

Crossrefs

Cf. A092938, A092939, A116619.

Programs

PARI

{for(n=1,56,k=2*prime(n);q=2;while(!isprime(p=k-q),q=nextprime(q+1));print1(p,","))} \\ Klaus Brockhaus, Dec 23 2006

Formula

a(n) = 2*prime(n) - A092938(n).

Extensions

Edited and extended by Klaus Brockhaus, Dec 23 2006