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A076845 Least k>0 such that n^k + n - 1 is prime.

%I A076845 #18 Apr 07 2025 14:27:52
%S A076845 1,1,1,2,1,1,2,1,1,2,1,2,16,1,1,4,3,1,2,1,1,4,1,3,2,1,2,10,1,1,108,3,
%T A076845 1,2,1,1,2,2,1,2,1,3,2,1,2,20,2,1,2,1,1,2,1,1,2,1,4,2,2,7,8,3,1,2,1,
%U A076845 24,2,1,1,12,4,3,8,1,1,4,3,1,194,3,1,2,1,2,2,1,8,2,1,1,4,2,2,54,1,1,4,1,1
%N A076845 Least k>0 such that n^k + n - 1 is prime.
%C A076845 From _Robert Israel_, Apr 07 2025: (Start)
%C A076845 No terms == 5 (mod 6), as x^k + x - 1 is divisible by x^2 - x - 1 when k == 5 (mod 6).
%C A076845 a(113) > 7000 if it exists. (End)
%H A076845 Robert Israel, <a href="/A076845/a076845.txt">Incomplete table of n, a(n) for n = 2 .. 1000</a>. -1 denotes a value that is > 3000 if it exists.
%p A076845 f:= proc(n) local k;
%p A076845     for k from 1 do if isprime(n^k+n-1) then return k fi od
%p A076845 end proc:
%p A076845 map(f, [$2..112]); # _Robert Israel_, Apr 07 2025
%t A076845 lk[n_]:=Module[{k=1},While[!PrimeQ[n^k+n-1],k++];k]; Array[lk,100,2] (* _Harvey P. Dale_, Jun 29 2017 *)
%o A076845 (PARI) a(n) = {my(k=1); while(!isprime(n^k+n-1), k++); k;} \\ _Michel Marcus_, Nov 29 2013
%o A076845 (Haskell)
%o A076845 a076845 n = head [k | k <- [1..], a010051'' (n ^ k + n - 1) == 1]
%o A076845 -- _Reinhard Zumkeller_, Jul 17 2014
%Y A076845 Cf. A078178, A076846.
%Y A076845 Cf. A010051.
%K A076845 nonn
%O A076845 2,4
%A A076845 _Benoit Cloitre_, Nov 20 2002