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Numbers k such that k^k*prime(k) - 1 is prime.
0

%I #27 Jan 05 2025 23:39:48

%S 2,6,40,56,954

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

%C a(6) > 22000. - _Giovanni Resta_, Jun 12 2017

%C a(6) > 40000. - _Michael S. Branicky_, Jan 05 2025

%e a(1) = 2 because 3*2^2-1 = 11 a prime.

%e a(2) = 6 because 13*6^6-1 = 606527 a prime.

%t Select[Range[1000], PrimeQ[Prime[#] #^# - 1] &]

%o (Magma) [n: n in [1..1000] | IsPrime(NthPrime(n)*n^n-1)];

%Y Cf. A086173.

%K nonn,more

%O 1,1

%A _Vincenzo Librandi_, Jun 10 2017