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Coefficients of monic primitive irreducible polynomials over GF(5) listed in lexicographic order.
11

%I #12 Sep 10 2019 03:18:14

%S 12,13,112,123,133,142,1032,1033,1042,1043,1102,1113,1143,1203,1213,

%T 1222,1223,1242,1302,1312,1322,1323,1343,1403,1412,1442,10122,10123,

%U 10132,10133,10412,10413,10442,10443,11013,11023,11032,11042,11113

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

%H T. D. Noe, <a href="/A058950/b058950.txt">Table of n, a(n) for n=1..354</a> (through degree 5)

%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 5.

%t car = 5; maxDegree = 5;

%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. A058945.

%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