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Primes of the form k^k + k^3 + 1.
1

%I #27 Sep 08 2022 08:45:25

%S 2,3,13,3251,16777729,387421219,11112006825560761,

%T 443426488243037769948249630619149912487,

%U 1075911801979993982060429252856123779115487368830416064665177

%N Primes of the form k^k + k^3 + 1.

%C The values of k such that k^k + k^2 + 1 is prime are 0, 1, 2, 5, 8, 9, 14, 27, 38, 62, 255, (4000), .... per _Vincenzo Librandi_'s extension, 2 is an element iff one defines 0^0 = 1.

%H Charles R Greathouse IV, <a href="/A119987/b119987.txt">Table of n, a(n) for n = 1..11</a>

%t f[n_] := (n^n + n^3 + 1); Select[f@ Range@ 40, PrimeQ]

%o (Magma) [ a: n in [0..250] | IsPrime(a) where a is n^n+n^3+1 ]; // _Vincenzo Librandi_, Dec 22 2010

%o (PARI) for(n=1, 255, if(ispseudoprime(t=n^n+n^3+1), print1(t", "))); v \\ _Charles R Greathouse IV_, Feb 17 2011

%Y Cf. A000040, A120479, A120480, A119264, A119448.

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 03 2006

%E 2 added by _Vincenzo Librandi_, Dec 22 2010