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 A019587 The left budding sequence: # of i such that 0
 1, 1, 3, 2, 1, 5, 3, 8, 5, 2, 9, 5, 1, 10, 5, 15, 9, 3, 15, 8, 21, 13, 5, 20, 11, 2, 19, 9, 27, 16, 5, 25, 13, 1, 23, 10, 33, 19, 5, 30, 15, 41, 25, 9, 37, 20, 3, 33, 15, 46, 27, 8, 41, 21, 55, 34, 13, 49, 27, 5, 43, 20, 59, 35, 11, 52, 27, 2, 45, 19, 63, 36, 9, 55, 27, 74, 45, 16, 65 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS REFERENCES J. H. Conway, personal communication. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 N. J. A. Sloane, Classic Sequences EXAMPLE {r}=0.61...; {2r}=0.23...; {3r}=0.85...; {4r}=0.47...; so that a(4)=2. MATHEMATICA r = GoldenRatio; p[x_] := FractionalPart[x]; u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0] v[n_, k_] := If[p[k*r] > p[n*r], 1, 0] s[n_] := Sum[u[n, k], {k, 1, n}] t[n_] := Sum[v[n, k], {k, 1, n}] Table[s[n], {n, 1, 100}]  (* A019587 *) Table[t[n], {n, 1, 100}]  (* A194733 *) (* Clark Kimberling, Sep 02 2011 *) PROG (Haskell) a019587 n = length \$ filter (<= nTau) \$             map (snd . properFraction . (* tau) . fromInteger) [1..n]    where (_, nTau) = properFraction (tau * fromInteger n)          tau = (1 + sqrt 5) / 2 -- Reinhard Zumkeller, Jan 28 2012 CROSSREFS Cf. A019588, A194733, A193738. Sequence in context: A171746 A113977 A183162 * A102427 A080883 A021315 Adjacent sequences:  A019584 A019585 A019586 * A019588 A019589 A019590 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Extended by Ray Chandler, Apr 18 2009 STATUS approved

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Last modified January 17 06:34 EST 2019. Contains 319207 sequences. (Running on oeis4.)