A078496 Smallest prime p such that p>n and 2*n-p is also prime.

5, 7, 7, 11, 11, 11, 13, 17, 13, 19, 17, 17, 19, 23, 19, 31, 23, 23, 31, 29, 29, 31, 29, 31, 37, 41, 31, 43, 41, 37, 37, 41, 41, 43, 47, 41, 43, 53, 43, 67, 47, 47, 61, 53, 53, 61, 53, 59, 61, 59, 61, 67, 59, 61, 73, 71, 61, 79, 71, 67, 67, 71, 71, 73, 83, 71, 73, 83, 73, 79

Offset: 4

Author

Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), Nov 26 2002

Keywords

• nonn

Comments

Suggested by Goldbach Conjecture.

Values of q from A143697. This follows from the factorization n^2-k^2 = (n-k)(n+k).

Examples

			a(11)=17.
		

Links

• P. CAMI, Table of n, a(n) for n = 4..60000

Crossrefs

Cf. A143697, A078587.

a(n) = 2n - A078587(n).

Cf. A082467

Programs

Mathematica

Table[p=n+1; q=2n-p; While[q>0&&!(PrimeQ[p]&&PrimeQ[q]), p++; q-- ]; p, {n, 4, 100}]

PARI

a(n) = {my(p=nextprime(n+1)); while(!isprime(2*n-p), p = nextprime(p+1)); p;} \\ Michel Marcus, Oct 22 2016

Formula

n>3 integer; a(n)=min{p: p>n; p, 2*n-p are primes}.

Extensions

Edited by N. J. A. Sloane, Jan 24 2009 at the suggestion of R. J. Mathar and T. D. Noe.