A076845 - OEIS

%I #18 Apr 07 2025 14:27:52

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

%C From _Robert Israel_, Apr 07 2025: (Start)

%C No terms == 5 (mod 6), as x^k + x - 1 is divisible by x^2 - x - 1 when k == 5 (mod 6).

%C a(113) > 7000 if it exists. (End)

%H 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 f:= proc(n) local k;

%p     for k from 1 do if isprime(n^k+n-1) then return k fi od

%p end proc:

%p map(f, [$2..112]); # _Robert Israel_, Apr 07 2025

%t lk[n_]:=Module[{k=1},While[!PrimeQ[n^k+n-1],k++];k]; Array[lk,100,2] (* _Harvey P. Dale_, Jun 29 2017 *)

%o (PARI) a(n) = {my(k=1); while(!isprime(n^k+n-1), k++); k;} \\ _Michel Marcus_, Nov 29 2013

%o (Haskell)

%o a076845 n = head [k | k <- [1..], a010051'' (n ^ k + n - 1) == 1]

%o -- _Reinhard Zumkeller_, Jul 17 2014

%Y Cf. A078178, A076846.

%Y Cf. A010051.

%K nonn

%O 2,4

%A _Benoit Cloitre_, Nov 20 2002