A328209 Numbers m such that m and m+1 are consecutive Zeckendorf-Niven numbers (A328208).

1, 2, 3, 4, 5, 12, 13, 21, 26, 55, 68, 80, 89, 92, 93, 110, 152, 183, 195, 207, 233, 236, 237, 254, 291, 304, 327, 364, 377, 380, 381, 398, 435, 471, 484, 555, 584, 605, 609, 639, 644, 759, 795, 834, 875, 894, 930, 987, 992, 1004, 1011, 1028, 1047, 1076, 1220

Offset: 1

Author

Amiram Eldar, Oct 07 2019

Keywords

• nonn

Examples

			12 is in the sequence since both 12 and 13 are in A328208: A007895(12) = 3 is a divisor of 12, and A007895(13) = 1 is a divisor of 13.
		

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, 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, {2}]; While[c < 60, If[aQ[k], v = Join[Rest[v], {k}]; If[AllTrue[Differences[v], # == 1 &], c++; AppendTo[s, k - 1]]]; k++]; s (* after Alonso del Arte at A007895 *)