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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A102062 A164584 A156432 * A308565 A341106 A203754

Adjacent sequences: A070017 A070018 A070019 * A070021 A070022 A070023

Keyword

easy,nonn,changed

Author

Labos Elemer, May 07 2002

Status

approved