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

1,1

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

Links

Table of n, a(n) for n=1..66.

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 *)

Prog

(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))<n-1) \\ Charles R Greathouse IV, Oct 16 2012

Crossrefs

Cf. A002326, A001122, A216838.

Sequence in context: A074764 A101087 A138887 * A031949 A043693 A043593

Adjacent sequences: A216842 A216843 A216844 * A216846 A216847 A216848

Keyword

nonn

Author

V. Raman, Sep 17 2012

Status

approved