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A194871
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Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=sqrt(6).
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4
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1, 1, 2, 3, 1, 2, 3, 1, 4, 2, 5, 3, 1, 4, 2, 5, 3, 1, 6, 4, 2, 7, 5, 3, 1, 6, 4, 2, 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, 3, 1, 10, 8, 6, 4, 2, 9, 7, 5, 3, 1, 10, 8, 6, 4, 2, 11, 9, 7, 5, 3, 12, 1, 10, 8, 6, 4, 2, 11, 9, 7, 5, 3, 12, 1, 10, 8, 6, 4, 13, 2, 11, 9, 7, 5
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OFFSET
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1,3
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COMMENTS
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See A194832 for a general discussion.
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LINKS
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Table of n, a(n) for n=1..94.
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EXAMPLE
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First nine rows:
1
1 2
3 1 2
3 1 4 2
5 3 1 4 2
5 3 1 6 4 2
7 5 3 1 6 4 2
7 5 3 1 8 6 4 2
9 7 5 3 1 8 6 4 2
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MATHEMATICA
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r = Sqrt[6];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]] (* A194871 *)
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}]] (* A194872 *)
q[n_] := Position[p, n]; Flatten[
Table[q[n], {n, 1, 80}]] (* A194873 *)
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CROSSREFS
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Cf. A194832, A194872, A194873.
Sequence in context: A194832 A195107 A054073 * A194899 A228094 A059832
Adjacent sequences: A194868 A194869 A194870 * A194872 A194873 A194874
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Sep 04 2011
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STATUS
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approved
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