A078587 Largest prime p such that p

3, 3, 5, 3, 5, 7, 7, 5, 11, 7, 11, 13, 13, 11, 17, 7, 17, 19, 13, 17, 19, 19, 23, 23, 19, 17, 29, 19, 23, 29, 31, 29, 31, 31, 29, 37, 37, 29, 41, 19, 41, 43, 31, 41, 43, 37, 47, 43, 43, 47, 47, 43, 53, 53, 43, 47, 59, 43, 53, 59, 61, 59, 61, 61, 53, 67, 67, 59, 71, 67, 59, 71

Offset: 4

Author

T. D. Noe, Dec 02 2002

Keywords

• easy
• nonn

Comments

Suggested by Goldbach Conjecture.

Also, values of p from A143697. This follows from the factorization n^2-k^2 = (n-k)(n+k). - T. D. Noe, Jan 22 2009

Links

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

Crossrefs

Cf. A143697, A078496.

Cf. A082467.

Programs

Mathematica

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

PARI

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

Formula

a(n) = 2n - A078496(n)

Extensions

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