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A207871 Numbers matched to Zeckendorf polynomials divisible by x^2 + 1. 3
4, 7, 11, 18, 22, 29, 33, 36, 47, 51, 54, 58, 76, 80, 83, 87, 94, 116, 123, 127, 130, 134, 141, 145, 152, 156, 163, 174, 188, 192, 199, 203, 206, 210, 217, 221, 228, 232, 235, 246, 250, 253, 264, 282, 304, 311, 322, 326, 329, 333, 340, 344, 351, 355 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Zeckendorf polynomials Z(x,n) are defined and ordered at A207813.

LINKS

Table of n, a(n) for n=1..54.

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}]

t2 = Table[p[n, x] /. x -> I, {n, 1, 420}];

Flatten[Position[t2, 0]                (* A207871 *)

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.

Sequence in context: A133257 A156039 A310767 * A023666 A023502 A274286

Adjacent sequences:  A207868 A207869 A207870 * A207872 A207873 A207874

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 21 2012

STATUS

approved

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Last modified May 14 13:45 EDT 2021. Contains 343884 sequences. (Running on oeis4.)