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Coefficients of monic primitive irreducible polynomials over GF(3) listed in lexicographic order.
11

%I #13 Sep 29 2020 17:01:16

%S 11,112,122,1021,1121,1201,1211,10012,10022,11002,11122,11222,12002,

%T 12112,12212,100021,100211,101011,101201,101221,102101,102211,110021,

%U 110101,110111,111011,111121,111211,112001,112111,112201,120001,120011

%N Coefficients of monic primitive irreducible polynomials over GF(3) listed in lexicographic order.

%C Church's table extends through degree 7.

%H T. D. Noe, <a href="/A058949/b058949.txt">Table of n, a(n) for n=1..561</a> (through degree 8)

%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.

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

%t car = 3; maxDegree = 8;

%t okQ[{1, 1}] = True;

%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 09 2019 *)

%Y Cf. A058944.

%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