A129832 Integers n such that the n-th cyclotomic polynomial Phi(n) is irreducible over GF(2).

1, 2, 3, 5, 6, 9, 10, 11, 13, 18, 19, 22, 25, 26, 27, 29, 37, 38, 50, 53, 54, 58, 59, 61, 67, 74, 81, 83, 101, 106, 107, 118, 121, 122, 125, 131, 134, 139, 149, 162, 163, 166, 169, 173, 179, 181, 197, 202, 211, 214, 227, 242, 243, 250, 262, 269, 278, 293

Offset

1,2

Links

Table of n, a(n) for n=1..58.

Formula

This sequence consists of 1, 2 and numbers having primitive root 2 (that is, numbers that are powers of primes p in sequence A001122, or twice powers of p). - T. D. Noe, Jan 03 2008

Example

7 is absent from the list as Phi(7) == (x^3 + x + 1)*(x^3 + x^2 + 1) (mod 2).

Mathematica

Select[Range[300], Transpose[Rest[FactorList[Cyclotomic[#, x], Modulus -> 2]]][[2]] == {1} &] (* T. D. Noe, Mar 03 2014 *)

Prog

(PARI) for(x=1, 200, if(polisirreducible(Mod(1, 2)*polcyclo(x)), print1(x", ")))

Crossrefs

Sequence in context: A162923 A107040 A045989 * A166687 A189224 A018762

Adjacent sequences: A129829 A129830 A129831 * A129833 A129834 A129835

Keyword

easy,nonn

Author

Phil Carmody, May 21 2007

Status

approved