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A207671 Numbers in ternary representation that match nonzero polynomials with all coefficients in {0,1,2} that are irreducible modulo 3. 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 (list; graph; refs; listen; history; text; internal format)
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 A235828

Adjacent sequences:  A207668 A207669 A207670 * A207672 A207673 A207674

KEYWORD

nonn,base

AUTHOR

Clark Kimberling, Feb 26 2012

STATUS

approved

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Last modified January 21 15:30 EST 2022. Contains 350479 sequences. (Running on oeis4.)