

A153439


Numbers k such that k^6 + k^3 + 1 is prime.


10



1, 2, 3, 8, 11, 20, 21, 26, 30, 50, 51, 56, 60, 78, 98, 102, 117, 129, 134, 146, 159, 171, 186, 189, 191, 198, 200, 209, 210, 212, 222, 240, 249, 267, 269, 278, 279, 299, 300, 333, 344, 363, 383, 390, 398, 399, 425, 429, 438, 444, 450, 458, 504, 509, 533, 540
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

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]


LINKS

Pierre CAMI, Table of n, a(n) for n = 1..37835
Pantelis A. Damianou, On prime values of cyclotomic polynomials, arXiv:1101.1152 [math.NT], 2011.


MATHEMATICA

Select[Range@ 600, PrimeQ[#^6 + #^3 + 1] &] (* Michael De Vlieger, Jan 22 2018 *)


PROG

(MAGMA) [n: n in [0..500]  IsPrime(n^3*(n^3+1)+1)] // Vincenzo Librandi, Nov 26 2010
(PARI) is(n)=prime(n^6+n^3+1) \\ Charles R Greathouse IV, Feb 17 2017


CROSSREFS

Cf. A153438, A164989.
Sequence in context: A042443 A042263 A280323 * A289752 A119064 A285113
Adjacent sequences: A153436 A153437 A153438 * A153440 A153441 A153442


KEYWORD

nonn


AUTHOR

Pierre CAMI, Dec 26 2008


EXTENSIONS

Some unclear comments deleted by N. J. A. Sloane, Sep 06 2009
More terms from Vincenzo Librandi, Mar 25 2010


STATUS

approved



