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%I #11 Jan 10 2022 11:41:21
%S 3,4,6,9,31,187,632,2972
%N Numbers k such that k*(k-1)^k-(k-1)*k^(k-1)-1 is prime.
%e a(1)=3 because 3*2^3-2*3^2-1=5 is prime, a(2)=4 because 4*3^4-3*4^3-1=131 is prime, a(3)=6 because 6*5^6-5*6^5-1=54869 is prime, a(4)=9 because 9*8^9-8*9^8-1=863585783 is prime.
%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*(k-1)**k - (k-1)*k**(k-1) - 1):
%o print(k, end=", ")
%o afind(200) # _Michael S. Branicky_, Jan 10 2022
%Y Cf. A191409 (associated primes).
%K nonn,hard
%O 1,1
%A _Juri-Stepan Gerasimov_, Jun 12 2011
%E a(8) from _Michael S. Branicky_, Jan 10 2022