A068000 Numbers k such that (k! + 1) == 0 ( mod prime(k) ).

1, 2, 5, 18, 63

Offset: 1

Author

Robert G. Wilson v, Feb 08 2002

Keywords

• nonn
• hard
• more

Comments

There are no other terms below 33333. Is 63 the last term? - Hauke Worpel (hw1(AT)email.com), May 24 2003

There are no other terms below 534000. - Rick L. Shepherd, May 26 2003

There are no other terms below 10^7. - Amiram Eldar, Apr 22 2025

Crossrefs

Cf. A067999, A066953.

Programs

Mathematica

Do[ If[ Mod[n! + 1, Prime[n]] == 0, Print[n]], {n, 1, 10000} ]

PARI

for(k=1, 33333, if( (k!+1)%prime(k)==0, print1(k, ", ")))

PARI

list(lim) = {my(k = 0, r = 1); forprime(p = 1, lim, k++; r *= k; if(!((r+1) % p), print1(k, ", ")));} \\ Amiram Eldar, Apr 22 2025