A103506 Smallest prime p such that 2n+1 = 2q + p for some odd prime q, or 0 if no such prime exists.

0, 0, 0, 3, 5, 3, 5, 3, 5, 7, 13, 3, 5, 3, 5, 7, 13, 3, 5, 3, 5, 7, 13, 3, 5, 7, 17, 11, 13, 3, 5, 3, 5, 7, 13, 11, 13, 3, 5, 7, 37, 3, 5, 3, 5, 7, 13, 3, 5, 7, 17, 11, 13, 3, 5, 7, 29, 11, 13, 3, 5, 3, 5, 7, 13, 11, 13, 3, 5, 7, 37, 3, 5, 3, 5, 7, 13, 11

Offset: 1

Author

Lei Zhou, Feb 09 2005

Keywords

• nonn

Examples

			For n < 4 there are no such primes, thus a(1)-a(3)=0.
For n=4, 2*4+1 = 9 = 2*3+3, thus a(4)=3.
For n=11, 2*11+1 = 23 = 2*5+13, thus a(11)=13.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

a(n)=0 if A103509(n)=0, otherwise A000040(A103509(n)).

Cf. A103151, A103152, A103153.

Programs

Mathematica

Join[{0,0,0}, Table[m=3; While[! (PrimeQ[m] && (((n-m)/2) > 2) && PrimeQ[(n-m)/2]), m=m+2]; m, {n, 9, 299, 2}]]

Scheme

(define (A103506 n) (let ((ind (A103509 n))) (if (zero? ind) 0 (A000040 ind)))) ;; Antti Karttunen, Jun 19 2007

Extensions

Edited by Antti Karttunen, Jun 19 2007