A073443 Numbers n such that n! - n - 1 is prime.

3, 4, 10, 12, 346

Offset

1,1

Comments

Clearly n <> 2 (mod 3). For n>3, n!-n, n!-n+1, ..., n!-3, n!-2 is a sequence of n-1 consecutive composite numbers. Additional terms are greater than 2000.

a(5) > 7500. - Michael S. Branicky, Mar 04 2021

Links

Table of n, a(n) for n=1..5.

Mathematica

Select[Range[3, 346], PrimeQ[#! - # - 1] &] (* Arkadiusz Wesolowski, Jan 04 2012 *)

Prog

(PARI) for(n=3, 2000, if(isprime(n!-n-1), print1(n, ", ")))
(Python)
from math import factorial
from sympy import isprime
def ok(n): return isprime(factorial(n) - n - 1)
print([m for m in range(3, 500) if ok(m)]) # Michael S. Branicky, Mar 04 2021

Crossrefs

Cf. A073444 (corresponding primes), A002982 (n!-1 is prime), A073308 (n!+n+1 is prime).

Sequence in context: A092434 A239632 A031367 * A257494 A302347 A092119

Adjacent sequences: A073440 A073441 A073442 * A073444 A073445 A073446

Keyword

nonn,hard,more

Author

Rick L. Shepherd, Jul 31 2002

Extensions

Offset corrected by Arkadiusz Wesolowski, Jan 04 2012

Status

approved