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 A194968 Fractalization of (1+[n/r]), where [ ]=floor, r=(1+sqrt(5))/2 (the golden ratio), and n>=1. 3
 1, 1, 2, 1, 3, 2, 1, 3, 4, 2, 1, 3, 4, 5, 2, 1, 3, 4, 6, 5, 2, 1, 3, 4, 6, 7, 5, 2, 1, 3, 4, 6, 8, 7, 5, 2, 1, 3, 4, 6, 8, 9, 7, 5, 2, 1, 3, 4, 6, 8, 9, 10, 7, 5, 2, 1, 3, 4, 6, 8, 9, 11, 10, 7, 5, 2, 1, 3, 4, 6, 8, 9, 11, 12, 10, 7, 5, 2, 1, 3, 4, 6, 8, 9, 11, 12, 13, 10, 7, 5, 2, 1, 3, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  The sequence (1+[n/r]) is A019446. LINKS MATHEMATICA r = GoldenRatio; p[n_] := 1 + Floor[n/r] Table[p[n], {n, 1, 90}]  (* A019446 *) g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]] f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]] f[20]  (* A194968 *) row[n_] := Position[f[30], n]; u = TableForm[Table[row[n], {n, 1, 5}]] v[n_, k_] := Part[row[n], k]; w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]  (* A194969 *) q[n_] := Position[w, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194970 *) CROSSREFS Cf. A194959, A019446, A194969, A194970. Sequence in context: A076291 A275015 A211189 * A194980 A323607 A194959 Adjacent sequences:  A194965 A194966 A194967 * A194969 A194970 A194971 KEYWORD nonn AUTHOR Clark Kimberling, Sep 07 2011 STATUS approved

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Last modified May 9 22:40 EDT 2021. Contains 343746 sequences. (Running on oeis4.)