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

1,4

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

Mathematica

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

Prog

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

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).

Sequence in context: A049613 A002373 A236569 * A162022 A318240 A262289

Adjacent sequences: A103150 A103151 A103152 * A103154 A103155 A103156

Keyword

nonn

Author

Lei Zhou, Feb 09 2005

Extensions

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

Definition corrected by Hugo Pfoertner, Sep 16 2011

Status

approved