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A054065
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Fractal sequence induced by tau: for k >= 1, let p(k) be the permutation of 1,2,...,k obtained by ordering the fractional parts {h*tau} for h=1,2,...,k; then juxtapose p(1),p(2),p(3),...
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10
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1, 2, 1, 2, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 9, 1, 6, 3, 8, 5, 10, 2, 7, 4, 9, 1, 6, 3, 8, 5, 10, 2, 7, 4, 9, 1, 6, 11, 3, 8, 5, 10, 2, 7, 12, 4, 9, 1, 6, 11, 3, 8, 13, 5, 10, 2, 7, 12, 4, 9, 1, 6, 11, 3, 8, 13, 5, 10, 2, 7, 12, 4, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| p(1)=(1); p(2)=(2,1); p(3)=(2,1,3); p(4)=(2,4,1,3).
As a triangular array (see A194832), first nine rows:
1
2 1
2 1 3
2 4 1 3
5 2 4 1 3
5 2 4 1 6 3
5 2 7 4 1 6 3
5 2 7 4 1 6 3 8
5 2 7 4 9 1 6 3 8
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MATHEMATICA
| r = (1 + Sqrt[5])/2;
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]] (* A054065 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13}, {k, 1, n}]] (* A054069 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A054068 *)
(* from Clark Kimberling, Sep 3 2011 *)
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CROSSREFS
| Position of 1 in p(k) is given by A019446. Position of k in p(k) is given by A019587. For related arrays and sequences, see A194832.
Sequence in context: A194902 A194874 A194835 * A194868 A139024 A154958
Adjacent sequences: A054062 A054063 A054064 * A054066 A054067 A054068
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Apr 18 2009
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