A070020 At these values of n 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

Links

Michael De Vlieger, Table of n, a(n) for n = 1..5000

Formula

n-1, n+1 and 1+n+n^2 are all primes.

Example

n=6: 5,7 and 43 are prime values of 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 *)

Crossrefs

Cf. A070155-A070157, A000068, A006313-A006316, A056993-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

Author

Labos Elemer, May 07 2002

Status

approved