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

Author

Lei Zhou, Feb 10 2005

Keywords

• nonn

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65539

Crossrefs

Cf. A049084, A103506.

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

Programs

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}]

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

Formula

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

Extensions

Edited by Antti Karttunen, Jun 19 2007