A241423 Largest number k > 0 such that n + k! is prime, or 0 if no such k exists.

1, 2, 1, 4, 1, 6, 0, 2, 1, 10, 1, 6, 0, 2, 1, 11, 1, 14, 0, 2, 1, 16, 0, 3, 0, 2, 1, 20, 1, 22, 0, 0, 0, 4, 1, 33, 0, 2, 1, 25, 1, 38, 0, 2, 1, 44, 0, 6, 0, 2, 1, 52, 0, 4, 0, 2, 1, 27, 1, 50, 0, 0, 0, 4, 1, 64, 0, 2, 1, 55, 1, 67, 0, 0, 0, 6, 1, 73, 0, 2, 1, 68, 0, 4, 0, 2, 1, 52, 0, 6

Offset: 2

Author

Derek Orr, Aug 08 2014

Keywords

• nonn

Comments

If k >= n, then n + k! is divisible by n and is not prime.

a(n) < A020639(n), because if prime p divides n then p divides n + k! for k >= p. - Robert Israel, Aug 10 2014

There is no term for n = 1 since factorial primes 1 + k! can probably be arbitrarily large (A002981 shows k values). - Jens Kruse Andersen, Aug 13 2014

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A245714, A125162.

Programs

Maple

a:= proc(n)
local k;
for k from min(numtheory:-factorset(n)) to 1 by -1 do
  if isprime(n+k!)  then return(k) fi
od:
0
end proc:
seq(a(n),n=2..100); # Robert Israel, Aug 10 2014

Mathematica

a[n_] := Module[{k}, For[k = FactorInteger[n][[1, 1]], k >= 1, k--, If[PrimeQ[n + k!], Return[k]]]; 0];
a /@ Range[2, 100] (* Jean-François Alcover, Jul 27 2020, after Maple *)

PARI

a(n)=forstep(k=n,1,-1,if(ispseudoprime(n+k!),return(k)))
n=2;while(n<150,print1(a(n),", ");n++)