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A058944
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Coefficients of monic irreducible polynomials over GF(3) listed in lexicographic order.
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15
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10, 11, 12, 101, 112, 122, 1021, 1022, 1102, 1112, 1121, 1201, 1211, 1222, 10012, 10022, 10102, 10111, 10121, 10202, 11002, 11021, 11101, 11111, 11122, 11222, 12002, 12011, 12101, 12112, 12121, 12212, 100021, 100022, 100112, 100211
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OFFSET
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1,1
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REFERENCES
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R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 555-557.
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LINKS
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EXAMPLE
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The first few are x, x+1, x+2; x^2+1, x^2+x+2, x^2+2x+2; ... Note that x is irreducible but not primitive.
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MAPLE
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N:= 100: # to get the first N terms
count:= 0:
for d from 1 while count < N do
for nn from 0 to 3^d-1 while count < N do
L:= convert(nn, base, 3);
P:= add(L[i]*x^(i-1), i=1..nops(L))+x^d;
if Irreduc(P) mod 3 then
count:= count+1;
A[count]:= add(L[i]*10^(i-1), i=1..nops(L))+10^d;
fi
od
od:
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MATHEMATICA
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A058944 = Union[ Reap[ Do[ a = Reverse[ IntegerDigits[n, 3]]; b = {0}; la = Length[a]; k = 1; While[k < la+1, b = Append[ b, a[[k]]*x^(k-1)]; k++]; b = Plus @@ b; c = Factor[ b, Modulus -> 3]; id = IntegerDigits[n, 3]; If[b == c && (id == {1, 0} || id[[-1]] != 0), Sow[ FromDigits[id] ] ], {n, 3, 300}]][[2, 1]]](* Jean-François Alcover, Feb 13 2012, after A058943 *)
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CROSSREFS
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Irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058943, this sequence, 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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STATUS
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approved
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