A096292 Primes p such that p!-1 is divisible by the next prime larger than p.

3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607

Offset

1,1

Comments

This sequence includes A001359 as a subset, since the lesser of twin primes always satisfy this relation. The smallest number in this sequence that is not in A001359 is 7841. The only other known differences are 594278556271608991 and 4259842839142238791410741595983041626644087433.

Links

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..600

Carlos Rivera, Puzzle 270.

Example

17 is here because 17!-1 is divisible by 19 and 19 is the next prime larger than 17.

Prog

(PARI) p=2; forprime(q=3, , prod(j=1, p, Mod(j, q)) == 1 && print1(p, ", "); p=q) \\ Jeppe Stig Nielsen, Oct 04 2019

Crossrefs

Cf. A001359, A286181.

Sequence in context: A054799 A093326 A001359 * A181747 A078864 A208574

Adjacent sequences: A096289 A096290 A096291 * A096293 A096294 A096295

Keyword

nonn

Author

Stuart Gascoigne (stuart.g(AT)scoigne.com), Jun 24 2004

Status

approved