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A058947
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Coefficients of primitive irreducible polynomials over GF(2) listed in lexicographic order.
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16
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11, 111, 1011, 1101, 10011, 11001, 100101, 101001, 101111, 110111, 111011, 111101, 1000011, 1011011, 1100001, 1100111, 1101101, 1110011, 10000011, 10001001, 10001111, 10010001, 10011101, 10100111, 10101011
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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 11.
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LINKS
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EXAMPLE
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The first few are x+1; x^2+x+1; x^3+x+1, x^3+x^2+1; ... Note that x is irreducible but not primitive.
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MATHEMATICA
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car = 2; maxDegree = 13;
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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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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