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 A207872 Denominator of Z(n,1/2), where Z(n,x) is the n-th Zeckendorf polynomial. 5
 1, 2, 4, 4, 8, 8, 8, 16, 16, 16, 16, 16, 32, 32, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 256, 256, 256, 256, 256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Zeckendorf polynomials Z(x,n) are defined and ordered at A207813.  Each power 2^k appears F(k+1) times, where F=A000045 (Fibonacci numbers). Conjecture: a(n) is also the reverse binarization of the Zeckendorf representation of n in base Fibonacci. For example, 11 = 1x8 + 0x5 +1x3 +0x2 + 0x1, so 11 =10100 in base Fibonacci. Now read that as binary but in reverse, 00101 = 101 = 5 = A207873(11). - George Beck, Sep 02 2020 LINKS Sajed Haque, Discriminators of Integer Sequences, Thesis, 2017, See p. 36. MATHEMATICA fb[n_] := Block[{k = Ceiling[Log[GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[fr, 1]; t = t - Fibonacci[k],     AppendTo[fr, 0]]; k--]; fr]; t = Table[fb[n],       {n, 1, 500}]; 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, 40}] Denominator[Table[p[n, x] /. x -> 1/2,    {n, 1, 120}]]                       (* A207872 *) Numerator[Table[p[n, x] /. x -> 1/2,    {n, 1, 120}]]                       (* A207873 *) CROSSREFS Cf. A207813, A207873. Sequence in context: A062383 A034583 A076347 * A140513 A265322 A188112 Adjacent sequences:  A207869 A207870 A207871 * A207873 A207874 A207875 KEYWORD nonn,frac AUTHOR Clark Kimberling, Feb 21 2012 STATUS approved

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Last modified May 14 07:13 EDT 2021. Contains 343879 sequences. (Running on oeis4.)