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

2,1

Comments

a(odd) = 1.

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A070689: a(n) = 3.

Sequence in context: A201681 A062174 A154754 * A374146 A277109 A359262

Adjacent sequences: A102365 A102366 A102367 * A102369 A102370 A102371

Keyword

nonn

Author

Reinhard Zumkeller, Feb 22 2005

Status

approved