%I #36 Dec 07 2012 15:43:11

%S 4,6,7,8,9,10,12,14,15,16,17,18,20,21,22,23,24,25,26,27,28,30,31,32,

%T 33,34,35,36,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,54,55,56,57,

%U 58,60,62,63,64,65,66,68,69,70,71,72,73,74,75,76,77,78,79

%N Numbers n such that the polynomial 1 + x + x^2 + x^3 + x^4 + ... + x^(n-1) is reducible over GF(2).

%C Alternately, the union of the composite numbers and the primes for which 2 is not a primitive root.

%C This is the complement of A001122 (primes for which 2 is a primitive root). - _V. Raman_, Dec 01 2012

%t reducibleQ[n_] := Module[{f = FactorList[Sum[x^i, {i, 0, n - 1}], Modulus -> 2]}, Length[f] > 2 || f[[2, 2]] > 1]; Select[Range[2, 100], reducibleQ] (* _T. D. Noe_, Sep 19 2012 *)

%o (PARI) for(i=4, 100, if(isprime(i), if(znorder(Mod(2, i))!=(i-1), print(i)), print(i))) \\ _V. Raman_, Oct 14 2012

%o (PARI) is(n)=n>3 && (!isprime(n) || znorder(Mod(2,n))<n-1) \\ _Charles R Greathouse IV_, Oct 16 2012

%Y Cf. A002326, A001122, A216838.

%K nonn

%O 1,1

%A _V. Raman_, Sep 17 2012