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A330711 Numbers that are both Zeckendorf-Niven numbers (A328208) and lazy-Fibonacci-Niven numbers (A328212). 6
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 (list; graph; refs; listen; history; text; internal format)
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: A293132 A098895 A266543 * A220219 A284456 A233968

Adjacent sequences:  A330708 A330709 A330710 * A330712 A330713 A330714

KEYWORD

nonn

AUTHOR

Amiram Eldar, Dec 27 2019

STATUS

approved

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Last modified May 25 07:56 EDT 2020. Contains 334585 sequences. (Running on oeis4.)