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

1,1

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.

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 *)

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.

Sequence in context: A085546 A041306 A058952 * A064003 A135123 A129476

Adjacent sequences: A058947 A058948 A058949 * A058951 A058952 A058953

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