A113165 Numbers that divide primorial numbers plus one (p#+1).

2, 3, 7, 19, 31, 59, 61, 73, 97, 131, 139, 149, 167, 173, 181, 211, 223, 271, 277, 307, 313, 317, 331, 347, 463, 467, 509, 571, 601, 673, 809, 827, 877, 881, 953, 983, 997, 1031, 1033, 1039, 1051, 1063, 1069, 1109, 1259, 1279, 1283, 1291, 1297, 1361, 1381

Offset: 1

Author

Franklin T. Adams-Watters, Jan 05 2006

Keywords

• easy
• nonn

Comments

The smallest composite member of the sequence is 1843 (19 * 97), which divides 17#+1 (19 * 97 * 277). Based on Euclid's proof that there are infinitely many primes.

Examples

			59 is in the sequence because 13#+1 = 30031 = 59 * 509.
		

Links

• Jeppe Stig Nielsen, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002110 (primorials), A018239 (primorial primes), A000945 (Euclid-Mullin sequence), A006862 (primorials plus one).

Programs

PARI

n=0;for(i=2,1e5,p=Mod(1,i);forprime(q=2,factor(i)[1,1],if(p==-1,print(n++," ",i);break());p*=q)) \\ Jeppe Stig Nielsen, Mar 25 2017