2,1

Row sums are:

{3, 5, 7, 3, 15, 11, 15, 15, 3, 23, 5, 17, 27, 21, 15,...}.

This procedure gives more than the types with two factors:

Mod[(x^Prime[n] + 1)/(x + 1),2]=f1(x)*f2(x);

In each case the program picks just the first factor.

The classic Golay factorization:

Factor[PolynomialMod[(x^23 + 1)/((x + 1)), 2], Modulus -> 2]

(1 + x + x^5 + x^6 + x^7 + x^9 + x^11)

(1 + x^2 + x^4 + x^5 + x^6 + x^10 + x^11)

The other one mentioned by Sloane and Conway in "Sphere Packings":

Factor[PolynomialMod[(x^47 + 1)/((x + 1)), 2], Modulus -> 2]

(1 + x + x^2 + x^3 + x^5 + x^6 + x^7 + x^9 + x^10 + x^12 + x^13 + x^14 + x^18 + x^19 + x^23)

(1 + x^4 + x^5 + x^9 +x^10 + x^11 + x^13 + x^14 + x^16 + x^17 + x^18 + x^20 +x^21 + x^22 + x^23)

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, pp. 231.

Mod[(x^Prime[n] + 1)/(x + 1),2]=Product[fi(x),{i,0,n}];

Out_(n,m)=coefficients(f1(x)).

{1, 1, 0, 1},

{1, 0, 0, 1, 1, 1, 0, 0, 1},

{1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1},

{1, 0, 1, 0, 0, 1},

{1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1},

{1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1},

{1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1},

{1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1},

{1, 1, 0, 0, 0, 0, 0, 0, 0, 1},

{1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1},

{1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1},

{1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1},

{1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1},

{1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1},

{1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1}

a = Flatten[Table[If[ ( Factor[PolynomialMod[(x^Prime[n] + 1)/((x + 1)), 2], Modulus -> 2] == PolynomialMod[(x^Prime[n] + 1)/((x + 1)), 2]) /. x -> 2, {}, FactorList[PolynomialMod[( x^Prime[n] + 1)/((x + 1)), 2], Modulus -> 2][[2]][[1]]], {n, 2, 30}]];

Table[CoefficientList[a[[n]], x], {n, 1, Length[a]}];

Flatten[%] Table[Apply[Plus, CoefficientList[a[[n]], x]], {n, 1, Length[a]}];

Sequence in context: A100672 A079559 A014577 this_sequence A131377 A077049 A124895

Adjacent sequences: A157923 A157924 A157925 this_sequence A157927 A157928 A157929

nonn,tabl

Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Mar 09 2009