cp's OEIS Frontend

A058944 Coefficients of monic irreducible polynomials over GF(3) listed in lexicographic order.

%I A058944 #21 Dec 21 2021 23:41:03
%S A058944 10,11,12,101,112,122,1021,1022,1102,1112,1121,1201,1211,1222,10012,
%T A058944 10022,10102,10111,10121,10202,11002,11021,11101,11111,11122,11222,
%U A058944 12002,12011,12101,12112,12121,12212,100021,100022,100112,100211
%N A058944 Coefficients of monic irreducible polynomials over GF(3) listed in lexicographic order.
%D A058944 R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 555-557.
%H A058944 Robert Israel and T. D. Noe, <a href="/A058944/b058944.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..1318 from T. D. Noe)
%H A058944 R. Church, <a href="http://www.jstor.org/stable/1968675">Tables of irreducible polynomials for the first four prime moduli</a>, Annals Math., 36 (1935), 198-209. Church's table extends through degree 7.
%e A058944 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.
%p A058944 N:= 100: # to get the first N terms
%p A058944 count:= 0:
%p A058944 for d from 1 while count < N do
%p A058944 for nn from 0 to 3^d-1 while count < N do
%p A058944   L:= convert(nn,base,3);
%p A058944   P:= add(L[i]*x^(i-1),i=1..nops(L))+x^d;
%p A058944   if Irreduc(P) mod 3 then
%p A058944      count:= count+1;
%p A058944      A[count]:= add(L[i]*10^(i-1),i=1..nops(L))+10^d;
%p A058944   fi
%p A058944   od
%p A058944 od:
%p A058944 seq(A[i],i=1..N); # _Robert Israel_, Jul 06 2016
%t A058944 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 *)
%Y A058944 Cf. A058943, A058945-A058948.
%Y A058944 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.
%K A058944 nonn,easy,nice
%O A058944 1,1
%A A058944 _N. J. A. Sloane_, Jan 13 2001
%E A058944 More terms from _David Wasserman_, May 23 2002