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A194983
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Fractalization of (1+[n/sqrt(5)]), where [ ]=floor.
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5
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1, 2, 1, 2, 3, 1, 2, 4, 3, 1, 2, 4, 5, 3, 1, 2, 4, 6, 5, 3, 1, 2, 4, 6, 7, 5, 3, 1, 2, 4, 6, 8, 7, 5, 3, 1, 2, 4, 6, 8, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 9, 7, 5, 3, 1, 2, 4, 6, 8, 11, 10, 9, 7, 5, 3, 1, 2, 4, 6, 8, 11, 12, 10, 9, 7, 5, 3, 1, 2, 4, 6, 8, 11, 13, 12, 10, 9, 7, 5, 3, 1, 2, 4, 6
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OFFSET
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1,2
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COMMENTS
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See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (1+[n/sqrt(5)]) is A194964.
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LINKS
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Table of n, a(n) for n=1..94.
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MATHEMATICA
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r = Sqrt[5]; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}] (* A194964 *)
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] (* A194983 *)
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}]] (* A194984 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A194985 *)
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CROSSREFS
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Cf. A194959, A194983, A194984, A194985.
Sequence in context: A194976 A195082 A210535 * A195073 A194987 A194917
Adjacent sequences: A194980 A194981 A194982 * A194984 A194985 A194986
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Sep 07 2011
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STATUS
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approved
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