A058950 Coefficients of monic primitive irreducible polynomials over GF(5) listed in lexicographic order.

12, 13, 112, 123, 133, 142, 1032, 1033, 1042, 1043, 1102, 1113, 1143, 1203, 1213, 1222, 1223, 1242, 1302, 1312, 1322, 1323, 1343, 1403, 1412, 1442, 10122, 10123, 10132, 10133, 10412, 10413, 10442, 10443, 11013, 11023, 11032, 11042, 11113

Offset: 1

Author

N. J. A. Sloane, Jan 13 2001

Keywords

• nonn
• easy
• nice

Links

• T. D. Noe, Table of n, a(n) for n=1..354 (through degree 5)
• R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209. Church's table extends through degree 5.

Crossrefs

Cf. A058945.

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 = 5; maxDegree = 5;
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 10 2019 *)

Extensions

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