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A328211 Starts of runs of 4 consecutive Zeckendorf-Niven numbers (A328208). 6
1, 2, 3, 123543, 124242, 545502, 1367583, 1856349, 2431230, 2465110, 2593590, 2783709, 3247389, 3479229, 3917823, 3942909, 4174749, 4303428, 4494390, 4920640, 5143830, 5710383, 6261309, 6493149, 6552903, 6956829, 7420509, 7470880, 8970948, 9107790, 9507069, 10952928 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Grundman proved that this sequence is infinite by showing the F(120k-6) + F(8) + F(6) + F(4) is a term for all k >= 1, where F(k) is the k-th Fibonacci number.

She also proved that the only starts of runs of 5 consecutive Zeckendorf-Niven numbers are 1 and 2.

LINKS

Table of n, a(n) for n=1..32.

Helen G. Grundman, Consecutive Zeckendorf-Niven and lazy-Fibonacci-Niven numbers, Fibonacci Quarterly, Vol. 45, No. 3 (2007), pp. 272-276.

EXAMPLE

1 is in the sequence since 1, 2, 3 and 4 are in A328208: A007895(1) = 1 is a divisor of 1, A007895(2) = 1 is a divisor of 2, A007895(3) = 1 is a divisor of 3, and A007895(4) = 2 is a divisor of 4.

MATHEMATICA

z[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]]; aQ[n_] := Divisible[n, z[n]]; c = 0; k = 1; s = {}; v = Table[-1, {4}]; While[c < 32, If[aQ[k], v = Join[Rest[v], {k}]; If[AllTrue[Differences[v], # == 1 &], c++; AppendTo[s, k - 3]]]; k++]; s (* after Alonso del Arte at A007895 *)

CROSSREFS

Cf. A005349, A007895, A141769, A328208.

Sequence in context: A216977 A331426 A300191 * A324154 A038537 A338404

Adjacent sequences:  A328208 A328209 A328210 * A328212 A328213 A328214

KEYWORD

nonn

AUTHOR

Amiram Eldar, Oct 07 2019

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)