A083663 Least k such that k*n!-1 is prime.

3, 2, 1, 1, 2, 1, 1, 5, 3, 4, 4, 1, 5, 1, 2, 9, 2, 30, 30, 5, 44, 2, 7, 13, 5, 3, 11, 2, 14, 1, 7, 1, 1, 30, 16, 22, 36, 1, 38, 13, 22, 6, 36, 17, 36, 40, 31, 25, 38, 13, 4, 32, 22, 154, 10, 27, 7, 121, 9, 33, 19, 19, 4, 26, 100, 18, 46, 75, 21, 11, 34, 75, 38, 7, 45, 3, 19, 13, 59, 39, 72

Offset: 1

Author

Benoit Cloitre, Jun 14 2003

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..600

Crossrefs

Cf. A035093, A053989, A084730.

Programs

Maple

f:= proc(n) local w,k;
w:= n!;
for k from 1 do
  if isprime(k*w-1) then return k fi
od
end proc:
map(f, [$1..100]); # Robert Israel, Nov 23 2023

Mathematica

lkp[n_]:=Module[{k=1,nf=n!},While[!PrimeQ[k*nf-1],k++];k]; Array[lkp,100] (* Harvey P. Dale, Apr 26 2025 *)

PARI

a(n)=if(n<1,0,k=1; while(isprime(k*n!-1)==0,k++); k)

Formula

a(n) = A053989(n!) = (A084730(n)+1)/n!. - Robert Israel, Nov 23 2023