A065315 Smallest prime divisor of n-th primorial + (n+1)-st prime.

5, 11, 37, 13, 23, 30047, 510529, 9699713, 127, 107, 433, 1093, 375569, 13082761331670077, 941879, 32589158477190044789, 1922760350154212639131, 4129, 92388407, 5879, 40729680599249024150621323549, 1783, 4903, 10279098043, 191, 131, 109, 163, 337, 20261, 673327, 6599, 181

Offset: 1

Author

Labos Elemer, Oct 29 2001

Keywords

• nonn

Examples

			For n=3, 3rd primorial=30, prime(4)=7, sum=37, so a(3)=37.
		

Links

• Tyler Busby, Table of n, a(n) for n = 1..84 (terms 1..79 from Sean A. Irvine)
• Romeo Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670, 2012-2023. - From N. J. A. Sloane, Jun 13 2012

Crossrefs

Cf. A002110, A000040, A006530, A057713, A002584, A002585, A051342, A060881.

See also A065314, A065316, A065317.

Programs

PARI

a(n) = vecmin(factor(prod(i=1, n, prime(i)) + prime(n+1))[,1]); \\ Michel Marcus, Aug 29 2019

Formula

a(n) = A020639(A002110(n) + A000040(n+1)).

a(n) = A020639(A060881(n)). - Michel Marcus, Sep 08 2023

Extensions

More terms from Michel Marcus, Aug 29 2019