A216845 Numbers n such that the polynomial 1 + x + x^2 + x^3 + x^4 + ... + x^(n-1) is reducible over GF(2).

4, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79

Offset: 1

Author

V. Raman, Sep 17 2012

Keywords

• nonn

Comments

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

This is the complement of A001122 (primes for which 2 is a primitive root). - V. Raman, Dec 01 2012

Crossrefs

Cf. A002326, A001122, A216838.

Programs

Mathematica

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 *)

PARI

for(i=4, 100, if(isprime(i), if(znorder(Mod(2, i))!=(i-1), print(i)), print(i))) \\ V. Raman, Oct 14 2012

PARI

is(n)=n>3 && (!isprime(n) || znorder(Mod(2,n))Charles R Greathouse IV, Oct 16 2012