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 A328940 Numbers k such that k divides A003754(k+1). 0
 1, 2, 3, 23, 31, 61, 62, 173075, 259698, 332429, 2147535, 21217059, 72517101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers that divide the value of their dual Zeckendorf representation (A104326) when read as a binary number. Analogous to A276488, with dual Zeckendorf representation instead of Zeckendorf representation (A014417). The corresponding values of A003754(k+1) are 1, 2, 3, 46, 62, 183, 186, 15576750, 28826478, 45542773, 534736215, 15934011309, 100218633582, ... and the corresponding quotients are 1, 1, 1, 2, 2, 3, 3, 90, 111, 137, 249, 751, 1382, ... a(14) > 3*10^9, if it exists. LINKS EXAMPLE 23 is in the sequence since the dual Zeckendorf representation of 23 is 101110 that equals 46 when read as a binary number, and 23|46. MATHEMATICA fb[n_] := Module[{k = Ceiling[Log[GoldenRatio, n * Sqrt]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[fr, 1]; t = t - Fibonacci[k], AppendTo[fr, 0]]; k-- ]; fr]; dz[n_] := Module[{v = fb[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}, v[[i[[1, 1]];; -1]]]]; aQ[n_] := Divisible[FromDigits[dz[n], 2], n]; Select[Range, aQ] (* after Robert G. Wilson v at A014417 and Ron Knott's Maple code at A104326 *) CROSSREFS Cf. A003754, A014417, A104326, A276488. Sequence in context: A068887 A260128 A220569 * A024764 A213971 A024773 Adjacent sequences:  A328937 A328938 A328939 * A328941 A328942 A328943 KEYWORD nonn,more AUTHOR Amiram Eldar, Oct 31 2019 STATUS approved

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Last modified May 22 11:06 EDT 2022. Contains 353949 sequences. (Running on oeis4.)