A377838 Let p = prime(n), then a(n) is the least prime q < p such that p * q# + 1 is prime.

2, 2, 3, 2, 3, 3, 5, 2, 2, 13, 3, 2, 5, 3, 2, 7, 3, 5, 5, 3, 5, 2, 2, 11, 3, 3, 3, 5, 2, 13, 2, 3, 7, 13, 3, 7, 7, 5, 2, 2, 3, 2, 5, 13, 11, 29, 5, 19, 5, 2, 2, 3, 2, 3, 3, 13, 3, 3, 2, 3, 2, 13, 3, 3, 5, 3, 5, 3, 7, 7, 2, 3, 3, 11, 5, 67, 3, 7, 17, 2, 7, 2, 7

Offset: 2

Author

Jeppe Stig Nielsen, Nov 09 2024

Keywords

• nonn

Comments

The notation q# means A034386(q).

Buhler, Crandall and Penk conjecture a(n) exists for all n > 1.

Examples

			For a(122), consider 673, the 122nd prime. Search for primes of form 673*2*3*5*7*...*q + 1. The first such prime appears at q=509 (and 509 is less than 673). Therefore a(122) = 509.
		

Links

• Jeppe Stig Nielsen, Table of n, a(n) for n = 2..10001
• J. P. Buhler, R. E. Crandall and M. A. Penk, Primes of the form n! ± 1 and 2 · 3 · 5 ··· p ± 1, Math. Comp. 38 (1982), 639-643.

Crossrefs

Cf. A034386.

Programs

PARI

a(n)=p=prime(n);m=p;forprime(q=2,p-1,m*=q;ispseudoprime(m+1)&&return(q));error("none")