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Numbers k such that k^(k+1)*(k+1)^k + 1 is prime.
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%I #16 Aug 24 2024 11:44:15

%S 1,2,14,22,120

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

%C a(6) > 10^3.

%C Numbers k such that A051443(k)+1 is prime. - _Michel Marcus_, Oct 08 2019

%C a(6) > 10^4, if it exists. - _Michael S. Branicky_, Aug 24 2024

%t Select[Range[120], PrimeQ[#^(# + 1)*(# + 1)^# + 1] &] (* _Amiram Eldar_, Oct 08 2019 *)

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

%Y Cf. A000040, A051443.

%K nonn,more

%O 1,2

%A _Juri-Stepan Gerasimov_, Oct 08 2019