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A058949 Coefficients of monic primitive irreducible polynomials over GF(3) listed in lexicographic order.

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%I A058949 #13 Sep 29 2020 17:01:16
%S A058949 11,112,122,1021,1121,1201,1211,10012,10022,11002,11122,11222,12002,
%T A058949 12112,12212,100021,100211,101011,101201,101221,102101,102211,110021,
%U A058949 110101,110111,111011,111121,111211,112001,112111,112201,120001,120011
%N A058949 Coefficients of monic primitive irreducible polynomials over GF(3) listed in lexicographic order.
%C A058949 Church's table extends through degree 7.
%H A058949 T. D. Noe, <a href="/A058949/b058949.txt">Table of n, a(n) for n=1..561</a> (through degree 8)
%H A058949 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 A058949 The first few are x+1; x^2+x+2, x^2+2x+2; ...
%t A058949 car = 3; maxDegree = 8;
%t A058949 okQ[{1, 1}] = True;
%t A058949 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 A058949 FromDigits /@ Select[Table[IntegerDigits[k, car], {k, car+1, car^(maxDegree + 1)}], okQ] (* _Jean-François Alcover_, Sep 09 2019 *)
%Y A058949 Cf. A058944.
%Y A058949 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 A058949 nonn,easy,nice
%O A058949 1,1
%A A058949 _N. J. A. Sloane_, Jan 13 2001
%E A058949 More terms from Jean Gaumont (jeangaum87(AT)yahoo.com), Apr 16 2006