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

1,1

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.

Links

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A005382 A195354 A244638 * A128025 A092064 A152609

Adjacent sequences: A113162 A113163 A113164 * A113166 A113167 A113168

Keyword

easy,nonn

Author

Franklin T. Adams-Watters, Jan 05 2006

Status

approved