|
%I #12 Sep 10 2019 03:18:22
%S 12,14,113,123,125,135,145,153,155,163,1032,1052,1062,1112,1124,1152,
%T 1154,1214,1242,1262,1264,1304,1314,1322,1334,1352,1354,1362,1422,
%U 1432,1434,1444,1504,1524,1532,1534,1542,1552,1564,1604,1612,1632,1644,1654
%N Coefficients of monic primitive irreducible polynomials over GF(7) listed in lexicographic order.
%H T. D. Noe, <a href="/A058951/b058951.txt">Table of n, a(n) for n=1..206</a> (through degree 4)
%H R. Church, <a href="http://www.jstor.org/stable/1968675">Tables of irreducible polynomials for the first four prime moduli</a>, Annals Math., 36 (1935), 198-209. Church's table extends through degree 3.
%t car = 7; maxDegree = 4;
%t okQ[coefs_List] := Module[{P}, P = coefs.x^Range[Length[coefs] - 1, 0, -1]; coefs[[1]] == 1 && IrreduciblePolynomialQ[P, Modulus -> car] && PrimitivePolynomialQ[P, car]];
%t FromDigits /@ Select[Table[IntegerDigits[k, car], {k, car+1, car^(maxDegree + 1)}], okQ] (* _Jean-François Alcover_, Sep 10 2019 *)
%Y Cf. A058946.
%Y 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.
%K nonn,easy,nice
%O 1,1
%A _N. J. A. Sloane_, Jan 13 2001
%E More terms from Jean Gaumont (jeangaum87(AT)yahoo.com), Apr 16 2006
|
