A103153 a(n) is the smallest odd prime p such that 2*n+1 = 2*p + A000040(k) for some k>1, or 0 if no such prime exists.

0, 0, 0, 3, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 7, 5, 3, 3, 5, 5, 3, 7, 3, 3, 5, 3, 7, 5, 3, 7, 5, 3, 3, 5, 5, 3, 7, 3, 3, 5, 5, 3, 7, 3, 19, 5, 3, 7, 5, 11, 3, 11, 3, 3, 5, 3, 3, 5, 3, 7, 5, 11, 7, 11, 11, 3, 11, 3, 13, 5, 3, 3, 5, 5, 7, 7, 3, 3, 5, 5, 3, 7, 5, 3, 7, 3, 13, 5, 3, 7, 5, 3, 3, 5, 5, 7, 7, 3

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=7, 2*7+1 = 15 = 2*5+5, thus a(7)=7.
		

Links

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

Crossrefs

a(n)=0 if A103507(n)=0, otherwise A000040(A103507(n)).

Cf. A103151, A103152, A002373.

Cf. A195352 (similar definition, but p=2 is allowed).

Programs

Mathematica

Do[m = 3; While[ ! (PrimeQ[m] && ((n - 2*m) > 2) && PrimeQ[n - 2*m]), m = m + 2]; Print[m], {n, 9, 299, 2}]

Scheme

(define (A103153 n) (let ((ind (A103507 n))) (if (zero? ind) 0 (A000040 ind))))

Extensions

Edited and Scheme code added by Antti Karttunen, Jun 19 2007

Definition corrected by Hugo Pfoertner, Sep 16 2011