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A073443
Numbers n such that n! - n - 1 is prime.
4
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
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
KEYWORD
nonn,hard,more
AUTHOR
Rick L. Shepherd, Jul 31 2002
EXTENSIONS
Offset corrected by Arkadiusz Wesolowski, Jan 04 2012
STATUS
approved