A119987 Primes of the form k^k + k^3 + 1.

2, 3, 13, 3251, 16777729, 387421219, 11112006825560761, 443426488243037769948249630619149912487, 1075911801979993982060429252856123779115487368830416064665177

Offset: 1

Author

Jonathan Vos Post, Aug 03 2006

Keywords

• nonn

Comments

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.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..11

Crossrefs

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

Programs

Magma

[ a: n in [0..250] | IsPrime(a) where a is n^n+n^3+1 ]; // Vincenzo Librandi, Dec 22 2010

Mathematica

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

PARI

for(n=1, 255, if(ispseudoprime(t=n^n+n^3+1), print1(t", "))); v \\ Charles R Greathouse IV, Feb 17 2011

Extensions

2 added by Vincenzo Librandi, Dec 22 2010