A058949 Coefficients of monic primitive irreducible polynomials over GF(3) listed in lexicographic order.

11, 112, 122, 1021, 1121, 1201, 1211, 10012, 10022, 11002, 11122, 11222, 12002, 12112, 12212, 100021, 100211, 101011, 101201, 101221, 102101, 102211, 110021, 110101, 110111, 111011, 111121, 111211, 112001, 112111, 112201, 120001, 120011

Offset

1,1

Comments

Church's table extends through degree 7.

Links

T. D. Noe, Table of n, a(n) for n=1..561 (through degree 8)

R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209.

Example

The first few are x+1; x^2+x+2, x^2+2x+2; ...

Mathematica

car = 3; maxDegree = 8;
okQ[{1, 1}] = True;
okQ[coefs_List] := Module[{P}, P = coefs.x^Range[Length[coefs]-1, 0, -1]; coefs[[1]] == 1 && IrreduciblePolynomialQ[P, Modulus -> car] && PrimitivePolynomialQ[P, car]];
FromDigits /@ Select[Table[IntegerDigits[k, car], {k, car+1, car^(maxDegree + 1)}], okQ] (* Jean-François Alcover, Sep 09 2019 *)

Crossrefs

Cf. A058944.

Irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058943, A058944, A058948, A058945, A058946. Primitive irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058947, A058949, A058952, A058950, A058951.

Sequence in context: A144784 A030175 A263805 * A378022 A119742 A075842

Adjacent sequences: A058946 A058947 A058948 * A058950 A058951 A058952

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Jan 13 2001

Extensions

More terms from Jean Gaumont (jeangaum87(AT)yahoo.com), Apr 16 2006

Status

approved