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A058944 Coefficients of monic irreducible polynomials over GF(3) listed in lexicographic order. 15
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; text; internal format)
OFFSET
1,1
REFERENCES
R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 555-557.
LINKS
Robert Israel and T. D. Noe, Table of n, a(n) for n = 1..10000 (n = 1..1318 from T. D. Noe)
R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209. Church's table extends through degree 7.
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.
MAPLE
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:
seq(A[i], i=1..N); # Robert Israel, Jul 06 2016
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]]](* Jean-François Alcover, Feb 13 2012, after A058943 *)
CROSSREFS
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: A239903 A244159 A171752 * A167178 A077677 A216502
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Jan 13 2001
EXTENSIONS
More terms from David Wasserman, May 23 2002
STATUS
approved

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)