A103507 a(n) = Least i > 1, such that 2n+1 = 2*A000040(i)+A000040(k) for some k>1, 0 if no such i exists.

0, 0, 0, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 4, 3, 2, 2, 3, 3, 2, 4, 2, 2, 3, 2, 4, 3, 2, 4, 3, 2, 2, 3, 3, 2, 4, 2, 2, 3, 3, 2, 4, 2, 8, 3, 2, 4, 3, 5, 2, 5, 2, 2, 3, 2, 2, 3, 2, 4, 3, 5, 4, 5, 5, 2, 5, 2, 6, 3, 2, 2, 3, 3, 4, 4, 2, 2, 3, 3, 2, 4, 3, 2, 4, 2, 6, 3, 2, 4, 3, 2, 2, 3, 3, 4, 4, 2, 2, 3, 2, 2, 3, 3, 4, 4, 5, 2

Offset

1,4

Links

Table of n, a(n) for n=1..108.

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 and 3=A000040(2), thus a(4)=2. For n=7, 2*7+1 = 15 = 2*5+5 and 5=A000040(3), thus a(7)=3.

Mathematica

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

Prog

(Scheme, with Aubrey Jaffer's SLIB Scheme library from http://www.swiss.ai.mit.edu/~jaffer/SLIB.html )
(define (A103507 n) (let loop ((i 2)) (let ((p1 (A000040 i))) (cond ((>= p1 n) 0) ((prime? (+ 1 (* 2 (- n p1)))) i) (else (loop (+ 1 i)))))))

Crossrefs

a(n) = A049084(A103153(n)), for n >= 4. Can be used to compute A103153 and A103508. Cf. A103509.

Sequence in context: A239141 A377758 A195352 * A219252 A290839 A346651

Adjacent sequences: A103504 A103505 A103506 * A103508 A103509 A103510

Keyword

nonn

Author

Lei Zhou, Feb 09 2005

Extensions

Edited, Scheme-code added and starting offset changed from 0 to 1 by Antti Karttunen, Jun 19 2007

Status

approved