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

1,1

Comments

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

Links

Table of n, a(n) for n=1..40.

Example

(See the Example section of A207669.)

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 *)

Crossrefs

Cf. A207669, A206073.

Sequence in context: A305130 A098395 A207968 * A154328 A112654 A362987

Adjacent sequences: A207668 A207669 A207670 * A207672 A207673 A207674

Keyword

nonn,base

Author

Clark Kimberling, Feb 26 2012

Status

approved