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A240532 Numbers k such that (k+1)^(k-1) - k is prime.

%I A240532 #34 Aug 07 2025 06:24:39
%S A240532 3,5,8,17,30,66,86,100,122,160,2282,6508
%N A240532 Numbers k such that (k+1)^(k-1) - k is prime.
%C A240532 a(13) >= 8394. - _J.W.L. (Jan) Eerland_, Dec 23 2021
%C A240532 a(13) >= 20000. - _Michael S. Branicky_, Sep 01 2024
%e A240532 3 is in the sequence since (3+1)^(3-1) - 3 = 4^2 - 3 = 13 is prime.
%t A240532 Select[Range[0, 500], PrimeQ[(# + 1)^(# - 1) - #] &]
%t A240532 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 A240532 (Magma) [n: n in [1..500] | IsPrime((n+1)^(n-1)-n)];
%o A240532 (PARI) is(n)=isprime((n+1)^(n-1)-n) \\ _Charles R Greathouse IV_, Jun 13 2017
%o A240532 (Python)
%o A240532 from sympy import isprime
%o A240532 def afind(limit, startk=1):
%o A240532     for k in range(startk, limit+1):
%o A240532         if isprime((k+1)**(k-1) - k): print(k, end=", ")
%o A240532 afind(200) # _Michael S. Branicky_, Aug 17 2021
%Y A240532 Cf. A238378.
%K A240532 nonn,more,hard
%O A240532 1,1
%A A240532 _Vincenzo Librandi_, Apr 13 2014
%E A240532 a(11) from _Michael S. Branicky_, Aug 17 2021