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

1,2

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.

Example

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.

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 *)

Crossrefs

Cf. A005349, A007895, A328208.

Sequence in context: A039007 A050745 A077375 * A250049 A132027 A306077

Adjacent sequences: A328206 A328207 A328208 * A328210 A328211 A328212

Keyword

nonn

Author

Amiram Eldar, Oct 07 2019

Status

approved