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

Author

N. J. A. Sloane, Jan 13 2001

Keywords

• nonn
• easy
• nice

Comments

Church's table extends through degree 7.

Examples

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

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.

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.

Programs

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 *)

Extensions

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