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 A182615 Greatest k such that floor(k/r^n)=n, where r = golden mean = (1+sqrt(5))/2. 1
 3, 7, 16, 34, 66, 125, 232, 422, 760, 1352, 2388, 4185, 7294, 12644, 21824, 37518, 64278, 109781, 186980, 317666, 538472, 910868, 1537896, 2592049, 4361786, 7328960, 12297712, 20608762, 34495530, 57675437, 96331168, 160737950, 267960664, 446321504, 742796604, 1235255433 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA For n>=3, a(n)=-1+A182614(n)+A000032(n), where A000032 is the sequence of Lucas numbers. Conjectures from Chai Wah Wu, Jan 12 2023: (Start) a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) - 2*a(n-4) + 2*a(n-5) + a(n-6) for n > 8. G.f.: x*(-x^7 - x^6 + 3*x^5 + 4*x^2 - x - 3)/((x - 1)*(x + 1)*(x^2 + x - 1)^2). (End) EXAMPLE The integers k satisfying floor(k/r^3)=3 are 13,14,15,16, so that a(3)=16. PROG (PARI) a(n) = floor(((1+sqrt(5))/2)^n*(n+1)) \\ David A. Corneth, May 07 2022 CROSSREFS Cf. A001622, A182614, A000032. Sequence in context: A002936 A014668 A354909 * A181893 A054455 A178455 Adjacent sequences: A182612 A182613 A182614 * A182616 A182617 A182618 KEYWORD nonn AUTHOR Clark Kimberling, Nov 22 2010 EXTENSIONS a(23) corrected by Andrey Zabolotskiy, May 07 2022 More terms from David A. Corneth, May 07 2022 STATUS approved

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Last modified March 27 20:39 EDT 2023. Contains 361575 sequences. (Running on oeis4.)