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A194862 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=(1+sqrt(3))/2. 5
1, 1, 2, 3, 1, 2, 3, 1, 4, 2, 3, 1, 4, 2, 5, 3, 6, 1, 4, 2, 5, 3, 6, 1, 4, 7, 2, 5, 3, 6, 1, 4, 7, 2, 5, 8, 3, 6, 9, 1, 4, 7, 2, 5, 8, 3, 6, 9, 1, 4, 7, 10, 2, 5, 8, 11, 3, 6, 9, 1, 4, 7, 10, 2, 5, 8, 11, 3, 6, 9, 1, 12, 4, 7, 10, 2, 5, 8, 11, 3, 6, 9, 1, 12, 4, 7, 10, 2, 13, 5, 8, 11, 3, 14 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A194832 for a general discussion.

LINKS

Table of n, a(n) for n=1..94.

EXAMPLE

First nine rows:

1

1 2

3 1 2

3 1 4 2

3 1 4 2 5

3 6 1 4 2 5

3 6 1 4 7 2 5

3 6 1 4 7 2 5 8

3 6 9 1 4 7 2 5 8

MATHEMATICA

r = (1 + Sqrt[3])/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}]]  (* A194862 *)

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}]]  (* A194863 *)

q[n_] := Position[p, n]; Flatten[Table[q[n],

{n, 1, 80}]]  (* A194864 *)

CROSSREFS

Cf. A194832, A194863, A194864.

Sequence in context: A194074 A175469 A239526 * A194832 A195107 A054073

Adjacent sequences:  A194859 A194860 A194861 * A194863 A194864 A194865

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 04 2011

STATUS

approved

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Last modified July 25 20:59 EDT 2021. Contains 346294 sequences. (Running on oeis4.)