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

1,4

Links

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

Example

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.

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}]]

Prog

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

Crossrefs

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

Cf. A103151, A103152, A103153.

Sequence in context: A010703 A107489 A152050 * A094929 A096634 A105439

Adjacent sequences: A103503 A103504 A103505 * A103507 A103508 A103509

Keyword

nonn

Author

Lei Zhou, Feb 09 2005

Extensions

Edited by Antti Karttunen, Jun 19 2007

Status

approved