This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333704 #15 Oct 12 2023 06:20:17
%S A333704 1,2,3,28,29,1119,6133,6134,1141774,6851892,6854270,6854271,6880561,
%T A333704 219181118,1113539751,1187863323,1200376103,1247070050,1247070068,
%U A333704 1247070100,1247070104,1247070130,1251287495,1252760510,1257001167,40920315565,41404469929,41473080530
%N 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.
%C A333704 The corresponding quotients are 1, 1, 1, 2, 2, 4, 5, 5, 8, ...
%H A333704 Amiram Eldar, <a href="/A333704/b333704.txt">Table of n, a(n) for n = 1..85</a> (terms below 10^13)
%e A333704 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.
%t A333704 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
%Y A333704 Cf. A007895, A014417, A095376, A114136, A333702, A333703, A333705.
%K A333704 nonn
%O A333704 1,2
%A A333704 _Amiram Eldar_, Apr 02 2020
%E A333704 More terms from _Amiram Eldar_, Oct 12 2023