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
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Jan 13 2001
EXTENSIONS
More terms from David Wasserman, May 23 2002
STATUS
approved