A070020 At these values of k the first, 2nd and 3rd cyclotomic polynomials all give prime numbers.

6, 12, 138, 150, 192, 348, 642, 1020, 1092, 1230, 1620, 1788, 1932, 2112, 2142, 2238, 2658, 2688, 2730, 3330, 3540, 3918, 4002, 4158, 5010, 5640, 6090, 6450, 6552, 6702, 7950, 8088, 9000, 9042, 9240, 9462, 9768, 10008, 10092, 10272, 10302, 10332

Offset: 1

Author

Labos Elemer, May 07 2002

Keywords

• easy
• nonn

Comments

Numbers k such that k-1, k+1 and k^2+k+1 are all primes.

Examples

			For k = 6: 5, 7 and 43 are prime values of the first 3 cyclotomic polynomials.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Michael De Vlieger)

Crossrefs

Cf. A070155, A070156, A070157, A000068, A006313, A006314, A006315, A006316, A056993, A056994, A056995, A005574, A057465, A057002, A070025, A070042.

Programs

Mathematica

psQ[n_]:=And@@PrimeQ[{n-1,n+1,n^2+n+1}]; Select[Range[11000],psQ] (* Harvey P. Dale, Nov 05 2011 *)
Select[Range[10500], AllTrue[Cyclotomic[Range@ 3, #], PrimeQ] &] (* Michael De Vlieger, Dec 08 2018 *)

PARI

is(k) = isprime(k-1) && isprime(k+1) && isprime(k^2+k+1); \\ Amiram Eldar, Sep 24 2024