A078587 Largest prime p such that p<n and 2n-p is also prime.

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

4,1

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A143697, A078496.

Cf. A082467.

Sequence in context: A204022 A131832 A255316 * A335074 A239931 A033558

Adjacent sequences: A078584 A078585 A078586 * A078588 A078589 A078590

Keyword

easy,nonn

Author

T. D. Noe, Dec 02 2002

Extensions

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

Status

approved