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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

%I #9 Aug 19 2021 10:56:46

%S 10,11,12,20,21,22,101,112,122,202,211,221,1021,1022,1102,1112,1121,

%T 1201,1211,1222,2011,2012,2102,2111,2122,2201,2212,2221,10012,10022,

%U 10102,10111,10121,10202,11002,11021,11101,11111,11122,11222

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

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

%e (See the Example section of A207669.)

%t t = Table[IntegerDigits[n, 3], {n, 1, 1000}];

%t b[n_] := Reverse[Table[x^k, {k, 0, n}]]

%t p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]

%t Table[p[n, x], {n, 1, 15}]

%t u = {}; Do[n++;

%t If[IrreduciblePolynomialQ[p[n, x], Modulus -> 3],

%t AppendTo[u, n]], {n, 1, 400}]

%t u (* A207669 *)

%t Complement[Range[200], %] (* A207670 *)

%t b[n_] := FromDigits[IntegerDigits[u, 3][[n]]]

%t Table[b[n], {n, 1, 50}] (* A207671 *)

%Y Cf. A207669, A206073.

%K nonn,base

%O 1,1

%A _Clark Kimberling_, Feb 26 2012

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Last modified August 11 07:13 EDT 2024. Contains 375059 sequences. (Running on oeis4.)