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A194908 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=-Pi. 4
1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 8, 7, 6, 5, 4, 3, 2, 9, 1, 8, 7, 6, 5, 4, 3, 10, 2, 9, 1, 8, 7, 6, 5, 4, 11, 3, 10, 2, 9, 1, 8, 7, 6, 5, 12, 4, 11, 3, 10, 2, 9, 1, 8, 7, 6, 13, 5, 12, 4, 11, 3, 10, 2, 9, 1, 8, 7, 14, 6 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194832 for a general discussion.

LINKS

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

EXAMPLE

First nine rows:

  1;

  2, 1;

  3, 2, 1;

  4, 3, 2, 1;

  5, 4, 3, 2, 1;

  6, 5, 4, 3, 2, 1;

  7, 6, 5, 4, 3, 2, 1;

  7, 6, 5, 4, 3, 2, 1, 8;

  7, 6, 5, 4, 3, 2, 9, 1, 8;

MATHEMATICA

r = -Pi;

t[n_] := Table[FractionalPart[k*r], {k, 1, n}];

f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@

Sort[t[n], Less]], {n, 1, 20}]]  (* A194908 *)

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}]]  (* A194909 *)

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

{n, 1, 80}]]  (* A194910 *)

CROSSREFS

Cf. A194832, A194909, A194910.

Sequence in context: A226620 A194877 A102482 * A004736 A200370 A200443

Adjacent sequences:  A194905 A194906 A194907 * A194909 A194910 A194911

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 05 2011

STATUS

approved

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Last modified September 25 11:29 EDT 2021. Contains 347654 sequences. (Running on oeis4.)