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

%I #11 Apr 10 2016 10:16:34

%S 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,

%T 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,

%U 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

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

%C a(odd) = 1.

%C Since n + 1 divides n^3 + 1, a(n) <= 3. - _Robert Israel_, Jun 15 2014

%H Robert Israel, <a href="/A102368/b102368.txt">Table of n, a(n) for n = 2..10000</a>

%e 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.

%p A102368:= proc(n)

%p if n::odd or not isprime(n+1) then 1

%p elif isprime(n^2+1) then 3 else 2

%p fi

%p end proc; # _Robert Israel_, Jun 15 2014

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

%Y Cf. A070689: a(n) = 3.

%K nonn

%O 2,1

%A _Reinhard Zumkeller_, Feb 22 2005