A102368 Smallest k>0 such that n^k + 1 is not prime.

3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2

Offset: 2

Author

Reinhard Zumkeller, Feb 22 2005

Keywords

• nonn

Comments

a(odd) = 1.

Since n + 1 divides n^3 + 1, a(n) <= 3. - Robert Israel, Jun 15 2014

Examples

			n=10: 10^1+1=11=A000040(5), 10^2+1=101=A000040(26), but 10^3+1=1001=7*11*13, therefore a(10)=3.
		

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A070689: a(n) = 3.

Programs

Maple

A102368:= proc(n)
  if n::odd or not isprime(n+1) then 1
    elif isprime(n^2+1) then 3 else 2
  fi
end proc; # Robert Israel, Jun 15 2014

Mathematica

sk[n_]:=Module[{k=1},While[PrimeQ[n^k+1],k++];k]; Array[sk,110,2] (* Harvey P. Dale, Apr 09 2016 *)