A103509 a(n) is the least j such that 2n+1 = 2*A000040(k) + A000040(j) for some k > 1, or 0 if no such j exists.

0, 0, 0, 2, 3, 2, 3, 2, 3, 4, 6, 2, 3, 2, 3, 4, 6, 2, 3, 2, 3, 4, 6, 2, 3, 4, 7, 5, 6, 2, 3, 2, 3, 4, 6, 5, 6, 2, 3, 4, 12, 2, 3, 2, 3, 4, 6, 2, 3, 4, 7, 5, 6, 2, 3, 4, 10, 5, 6, 2, 3, 2, 3, 4, 6, 5, 6, 2, 3, 4, 12, 2, 3, 2, 3, 4, 6, 5, 6, 2, 3, 4, 18, 2, 3, 4, 7, 5, 6, 2, 3, 4, 10, 5, 6, 15, 7, 2, 3, 4, 12, 2, 3, 2, 3

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65539

Formula

a(n) = A049084(A103506(n)), for n >= 4.

Example

For n < 4 there are no such primes, thus a(1)=a(2)=a(3)=0.
For n=4, 2*4+1 = 9 = 2*3+3 and 3=A000040(2), thus a(4)=2.
For n=11, 2*11+1 = 23 = 13+2*5 and 13=A000040(6), thus a(11)=6.

Mathematica

Do[m = 3; While[ ! (PrimeQ[m] && (((n - m)/2) > 2) && PrimeQ[(n - m)/2]), 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 (A103509 n) (let ((o (+ (* 2 n) 1))) (let loop ((i 2)) (let ((p2 (A000040 i))) (cond ((> p2 (- o 6)) 0) ((prime? (/ (- o p2) 2)) i) (else (loop (+ 1 i)))))))) -- Antti Karttunen, Jun 19 2007
(PARI) A103509(n) = if(n<=3, 0, my(o=n+n+1); for(i=2, oo, if(isprime((o-prime(i))/2), return(i)))); \\ Antti Karttunen, Mar 30 2021

Crossrefs

Cf. A049084, A103506.

Can be used to compute A103506 and A103510. Cf. A103507.

Sequence in context: A366912 A276090 A073820 * A361929 A252941 A069898

Adjacent sequences: A103506 A103507 A103508 * A103510 A103511 A103512

Keyword

nonn

Author

Lei Zhou, Feb 10 2005

Extensions

Edited by Antti Karttunen, Jun 19 2007

Status

approved