A207671 Numbers in ternary representation that match nonzero polynomials with all coefficients in {0,1,2} that are irreducible modulo 3.

10, 11, 12, 20, 21, 22, 101, 112, 122, 202, 211, 221, 1021, 1022, 1102, 1112, 1121, 1201, 1211, 1222, 2011, 2012, 2102, 2111, 2122, 2201, 2212, 2221, 10012, 10022, 10102, 10111, 10121, 10202, 11002, 11021, 11101, 11111, 11122, 11222

Offset: 1

Author

Clark Kimberling, Feb 26 2012

Keywords

• nonn
• base

Comments

For a discussion and examples in base-10 representation, see A207670. For the analogous sequence in base 2, see A206073.

Examples

			(See the Example section of A207669.)
		

Crossrefs

Cf. A207669, A206073.

Programs

Mathematica

t = Table[IntegerDigits[n, 3], {n, 1, 1000}];
b[n_] := Reverse[Table[x^k, {k, 0, n}]]
p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]
Table[p[n, x], {n, 1, 15}]
u = {}; Do[n++;
If[IrreduciblePolynomialQ[p[n, x], Modulus -> 3],
  AppendTo[u, n]], {n, 1, 400}]
u                           (* A207669 *)
Complement[Range[200], %]   (* A207670 *)
b[n_] := FromDigits[IntegerDigits[u, 3][[n]]]
Table[b[n], {n, 1, 50}]     (* A207671 *)