A328210 Starts of runs of 3 consecutive Zeckendorf-Niven numbers (A328208).

1, 2, 3, 4, 12, 92, 236, 380, 1850, 2630, 4184, 7010, 8183, 8360, 11944, 12754, 13550, 16024, 17710, 17714, 18710, 20628, 22323, 22624, 25564, 28910, 31506, 36463, 36484, 39746, 40368, 44694, 48244, 49294, 53543, 58910, 59164, 64743, 70398, 75024, 77874, 78184

Offset: 1

Author

Amiram Eldar, Oct 07 2019

Keywords

• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Helen G. Grundman, Consecutive Zeckendorf-Niven and lazy-Fibonacci-Niven numbers, Fibonacci Quarterly, Vol. 45, No. 3 (2007), pp. 272-276.

Crossrefs

Cf. A005349, A007895, A154701, A328208.

Programs

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, {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 *)