A208665 Numbers that match odd ternary polynomials; see Comments.

3, 6, 27, 30, 33, 54, 57, 60, 243, 246, 249, 270, 273, 276, 297, 300, 303, 486, 489, 492, 513, 516, 519, 540, 543, 546, 2187, 2190, 2193, 2214, 2217, 2220, 2241, 2244, 2247, 2430, 2433, 2436, 2457, 2460, 2463, 2484, 2487, 2490, 2673, 2676, 2679

Offset: 1

Author

Clark Kimberling, Feb 29 2012

Keywords

• base
• nonn

Comments

The ternary polynomials (having all coefficients in {0,1,2}) are enumerated at A207966. This sequence shows the numbers n for which p(n,-x)=-p(n,x).

Crossrefs

Cf. A037314, A207966, A338086 (ternary digit duplication).

Programs

Mathematica

t = Table[IntegerDigits[n, 3], {n, 1, 4000}];
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, 30}]
even = {}; Do[n++; If[(p[n, x] /. x -> -x) == p[n, x], AppendTo[even, n]], {n, 1600}];
even     (* A037314 for n >= 2 *)
odd = {}; Do[n++; If[(p[n, x] /. x -> -x) == -p[n, x], AppendTo[odd, n]], {n, 3900}];
odd      (* A208665 *)

PARI

a(n) = 3*fromdigits(digits(n,3),9); \\ Kevin Ryde, Oct 17 2020