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%I #8 Dec 29 2021 05:57:27
%S 1,2,3,4,12,92,236,380,1850,2630,4184,7010,8183,8360,11944,12754,
%T 13550,16024,17710,17714,18710,20628,22323,22624,25564,28910,31506,
%U 36463,36484,39746,40368,44694,48244,49294,53543,58910,59164,64743,70398,75024,77874,78184
%N Starts of runs of 3 consecutive Zeckendorf-Niven numbers (A328208).
%H Amiram Eldar, <a href="/A328210/b328210.txt">Table of n, a(n) for n = 1..10000</a>
%H Helen G. Grundman, <a href="https://www.fq.math.ca/Papers1/45-3/grundman.pdf">Consecutive Zeckendorf-Niven and lazy-Fibonacci-Niven numbers</a>, Fibonacci Quarterly, Vol. 45, No. 3 (2007), pp. 272-276.
%e 12 is in the sequence since 12, 13 and 14 are in A328208: A007895(12) = 3 is a divisor of 12, A007895(13) = 1 is a divisor of 13, and A007895(14) = 2 is a divisor of 14.
%t 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, {3}]; While[c < 50, If[aQ[k], v = Join[Rest[v], {k}]; If[AllTrue[Differences[v], # == 1 &], c++; AppendTo[s, k - 2]]]; k++]; s (* after _Alonso del Arte_ at A007895 *)
%Y Cf. A005349, A007895, A154701, A328208.
%K nonn
%O 1,2
%A _Amiram Eldar_, Oct 07 2019