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Integers n such that the n-th cyclotomic polynomial Phi(n) is irreducible over GF(2).
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%I #11 Mar 04 2014 03:12:27

%S 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,

%T 74,81,83,101,106,107,118,121,122,125,131,134,139,149,162,163,166,169,

%U 173,179,181,197,202,211,214,227,242,243,250,262,269,278,293

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

%F 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

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

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

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

%K easy,nonn

%O 1,2

%A _Phil Carmody_, May 21 2007