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A194871 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). 4
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 (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

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A194832, A194872, A194873.

Sequence in context: A194832 A195107 A054073 * A194899 A228094 A059832

Adjacent sequences:  A194868 A194869 A194870 * A194872 A194873 A194874

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 04 2011

STATUS

approved

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Last modified May 23 01:52 EDT 2022. Contains 353959 sequences. (Running on oeis4.)