A216842 Degree of the smallest irreducible polynomial factor for the polynomial (x^(2n+1)+1)/(x+1) over GF(2).

0, 2, 4, 3, 2, 10, 12, 2, 8, 18, 2, 11, 4, 2, 28, 5, 2, 3, 36, 2, 20, 14, 2, 23, 3, 2, 52, 4, 2, 58, 60, 2, 4, 66, 2, 35, 9, 2, 3, 39, 2, 82, 4, 2, 11, 3, 2, 4, 48, 2, 100, 51, 2, 106, 36, 2, 28, 4, 2, 3, 10, 2, 4, 7, 2, 130, 3, 2, 68, 138, 2, 10, 4, 2, 148

Offset

0,2

Links

Table of n, a(n) for n=0..74.

Mathematica

Join[{0}, Table[Exponent[FactorList[Sum[x^i, {i, 0, 2*n}], Modulus -> 2][[2, 1]], x], {n, 100}]] (* T. D. Noe, Sep 19 2012 *)

Prog

(PARI) vector(100, p, factormod((x^(2*p+1)+1)/(x+1), 2, 1)[1, 1])

Crossrefs

Cf. A002326, A001122.

Sequence in context: A084936 A365052 A308744 * A099066 A021415 A244646

Adjacent sequences: A216839 A216840 A216841 * A216843 A216844 A216845

Keyword

nonn

Author

V. Raman, Sep 17 2012

Status

approved