%I #34 Sep 08 2022 08:45:39
%S 1,2,3,8,11,20,21,26,30,50,51,56,60,78,98,102,117,129,134,146,159,171,
%T 186,189,191,198,200,209,210,212,222,240,249,267,269,278,279,299,300,
%U 333,344,363,383,390,398,399,425,429,438,444,450,458,504,509,533,540
%N Numbers k such that k^6 + k^3 + 1 is prime.
%C n^6+n^3+1 is the cyclotomic polynomial Phi(9,n). Damianou, p. 4, claims that there is strong experimental evidence that k^6 + k^3 + 1 is prime for infinitely many values of k. - _Jonathan Vos Post_, Jan 06 2011 [Comment corrected by _Jon E. Schoenfield_, Jan 22 2018]
%H Pierre CAMI, <a href="/A153439/b153439.txt">Table of n, a(n) for n = 1..37835</a>
%H Pantelis A. Damianou, <a href="http://arxiv.org/abs/1101.1152">On prime values of cyclotomic polynomials</a>, arXiv:1101.1152 [math.NT], 2011.
%t Select[Range@ 600, PrimeQ[#^6 + #^3 + 1] &] (* _Michael De Vlieger_, Jan 22 2018 *)
%o (Magma) [n: n in [0..500] | IsPrime(n^3*(n^3+1)+1)] // _Vincenzo Librandi_, Nov 26 2010
%o (PARI) is(n)=prime(n^6+n^3+1) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A153438, A164989.
%K nonn
%O 1,2
%A _Pierre CAMI_, Dec 26 2008
%E Some unclear comments deleted by _N. J. A. Sloane_, Sep 06 2009
%E More terms from _Vincenzo Librandi_, Mar 25 2010