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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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12
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209.
R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 555-557.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1318 (through degree 8)
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EXAMPLE
| 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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MATHEMATICA
| 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]]](* From Jean-François Alcover, Feb 13 2012, after A058943 *)
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CROSSREFS
| Cf. A058943, A058945-A058948.
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.
Sequence in context: A048002 A125098 A171752 * A167178 A077677 A107741
Adjacent sequences: A058941 A058942 A058943 * A058945 A058946 A058947
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KEYWORD
| nonn,easy,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 13 2001
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EXTENSIONS
| Church's table extends through degree 7.
More terms from David Wasserman (wasserma(AT)spawar.navy.mil), May 23 2002
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