OFFSET
1,1
COMMENTS
This is one possible generalization of "the least prime problem in special arithmetic progressions" when n in nk+1 is replaced by n!.
a(n) is the smallest prime p such that the multiplicative group modulo p has a subgroup of order n!. - Joerg Arndt, Oct 18 2020
LINKS
EXAMPLE
a(5)=241 because in arithmetic progression 120k+1=5!k+1 the second term is prime, 241.
MATHEMATICA
sp[n_]:=Module[{nf=n!, k=1}, While[!PrimeQ[nf*k+1], k++]; nf*k+1]; Array[sp, 20] (* Harvey P. Dale, Jan 27 2013 *)
PROG
(PARI) a(n) = for(k=1, oo, if(isprime(k*n! + 1), return(k*n! + 1))); \\ Daniel Suteu, Oct 18 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved