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

Author

Amiram Eldar, Dec 27 2019

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Intersection of A328208 and A328212.

Cf. A007895, A014417, A104326, A112310.

Programs

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[#]] &]