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A058949
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Coefficients of monic primitive irreducible polynomials over GF(3) listed in lexicographic order.
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11
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11, 112, 122, 1021, 1121, 1201, 1211, 10012, 10022, 11002, 11122, 11222, 12002, 12112, 12212, 100021, 100211, 101011, 101201, 101221, 102101, 102211, 110021, 110101, 110111, 111011, 111121, 111211, 112001, 112111, 112201, 120001, 120011
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OFFSET
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1,1
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COMMENTS
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Church's table extends through degree 7.
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LINKS
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EXAMPLE
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The first few are x+1; x^2+x+2, x^2+2x+2; ...
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MATHEMATICA
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car = 3; maxDegree = 8;
okQ[{1, 1}] = True;
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 09 2019 *)
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CROSSREFS
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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.
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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More terms from Jean Gaumont (jeangaum87(AT)yahoo.com), Apr 16 2006
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STATUS
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approved
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