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A333704 Numbers k such that the total number of 1's in the Zeckendorf representation of the first k integers is a multiple of k. 3
1, 2, 3, 28, 29, 1119, 6133, 6134, 1141774, 6851892, 6854270, 6854271, 6880561, 219181118, 1113539751, 1187863323, 1200376103, 1247070050, 1247070068, 1247070100, 1247070104, 1247070130, 1251287495, 1252760510, 1257001167 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The corresponding quotients are 1, 1, 1, 2, 2, 4, 5, 5, 8, ...

No more terms below 10^10.

LINKS

Table of n, a(n) for n=1..25.

EXAMPLE

3 is a term since the numbers 1, 2 and 3 in the Zeckendorf representation are 1, 10 and 100, and the sum of their numbers of digits of 1 is 1 + 1 + 1 = 3 which is divisible by 3.

MATHEMATICA

zeckSum[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]]; seq = {}; sum = 0; Do[sum += zeckSum[n]; If[Divisible[sum, n], AppendTo[seq, n]], {n, 1, 10^6}]; seq

CROSSREFS

Cf. A007895, A014417, A095376, A114136, A333702, A333703, A333705.

Sequence in context: A037316 A032813 A337560 * A104313 A279505 A279995

Adjacent sequences:  A333701 A333702 A333703 * A333705 A333706 A333707

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Apr 02 2020

STATUS

approved

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Last modified October 16 20:36 EDT 2021. Contains 348047 sequences. (Running on oeis4.)