A330711 Numbers that are both Zeckendorf-Niven numbers (A328208) and lazy-Fibonacci-Niven numbers (A328212).

1, 2, 4, 6, 12, 16, 30, 36, 48, 55, 60, 72, 78, 84, 90, 102, 105, 126, 144, 156, 168, 180, 184, 192, 208, 238, 240, 252, 264, 304, 315, 320, 322, 344, 360, 370, 378, 396, 430, 432, 488, 528, 536, 540, 576, 590, 605, 609, 621, 639, 648, 657, 660, 672, 680, 702

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

6 is in the sequence since A007895(6) = 2 and A112310(6) = 3, and both 2 and 3 are divisors of 6.

Mathematica

zeckSum[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]];
fibTerms[n_] := Module[{k = Ceiling[Log[GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[fr, 1]; t = t - Fibonacci[k], AppendTo[fr, 0]]; k--]; fr];
dualZeckSum[n_] := Module[{v = fibTerms[n]}, nv = Length[v]; i = 1; While[i <= nv - 2, If[v[[i]] == 1 && v[[i + 1]] == 0 && v[[i + 2]] == 0, v[[i]] = 0; v[[i + 1]] = 1; v[[i + 2]] = 1; If[i > 2, i -= 3]]; i++]; i = Position[v, _?(# > 0 &)]; If[i == {}, 0, Total[v[[i[[1, 1]] ;; -1]]]]];
Select[Range[1000], Divisible[#, zeckSum[#]] && Divisible[#, dualZeckSum[#]] &]

Crossrefs

Intersection of A328208 and A328212.

Cf. A007895, A014417, A104326, A112310.

Sequence in context: A098895 A266543 A378314 * A220219 A284456 A233968

Adjacent sequences: A330708 A330709 A330710 * A330712 A330713 A330714

Keyword

nonn

Author

Amiram Eldar, Dec 27 2019

Status

approved