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

4,1

Comments

Suggested by Goldbach Conjecture.

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

Links

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

Formula

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

Example

a(11)=17.

Mathematica

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

Prog

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

Crossrefs

Cf. A143697, A078587.

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

Cf. A082467

Sequence in context: A201459 A053672 A087525 * A114521 A258653 A159482

Adjacent sequences: A078493 A078494 A078495 * A078497 A078498 A078499

Keyword

nonn

Author

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

Extensions

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

Status

approved