A240532 - OEIS

%I #31 Sep 01 2024 13:08:43

%S 3,5,8,17,30,66,86,100,122,160,2282,6508

%N Numbers k such that (k+1)^(k-1) - k is prime.

%C a(13) >= 8394. - _J.W.L. (Jan) Eerland_, Dec 23 2021

%C a(13) >= 20000. - _Michael S. Branicky_, Sep 01 2024

%e 3 is in the sequence since (3+1)^(3-1) - 3 = 4^2 - 3 = 13 is prime.

%t Select[Range[0, 500], PrimeQ[(# + 1)^(# - 1) - #] &].

%t n=0;Monitor[Parallelize[While[True,If[PrimeQ[(n+1)^(n-1)-n],Print[n]];n++];n],n] (* _J.W.L. (Jan) Eerland_, Dec 23 2021 *)

%o (Magma) [n: n in [1..500] | IsPrime((n+1)^(n-1)-n)];

%o (PARI) is(n)=isprime((n+1)^(n-1)-n) \\ _Charles R Greathouse IV_, Jun 13 2017

%o (Python)

%o from sympy import isprime

%o def afind(limit, startk=1):

%o     for k in range(startk, limit+1):

%o         if isprime((k+1)**(k-1) - k): print(k, end=", ")

%o afind(200) # _Michael S. Branicky_, Aug 17 2021

%Y Cf. A238378.

%K nonn,more

%O 1,1

%A _Vincenzo Librandi_, Apr 13 2014

%E a(11) from _Michael S. Branicky_, Aug 17 2021