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

Author

Phil Carmody, May 21 2007

Keywords

• easy
• nonn

Examples

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

Programs

Mathematica

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

PARI

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

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