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A194905 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. 6
1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 9, 2, 3, 4, 5, 6, 7, 8, 1, 9, 2, 10, 3, 4, 5, 6, 7, 8, 1, 9, 2, 10, 3, 11, 4, 5, 6, 7, 8, 1, 9, 2, 10, 3, 11, 4, 12, 5, 6, 7, 8, 1, 9, 2, 10, 3, 11, 4, 12, 5, 13, 6, 7, 8, 1, 9 (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

1 2 3

1 2 3 4

1 2 3 4 5

1 2 3 4 5 6

1 2 3 4 5 6 7

8 1 2 3 4 5 6 7

8 1 9 2 3 4 5 6 7

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}]]  (* A194905 *)

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}]]  (* A194906 *)

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

{n, 1, 80}]]  (* A194907 *)

CROSSREFS

Cf. A194832, A194906, A194907.

Sequence in context: A140756 A002260 A243732 * A243730 A133994 A066041

Adjacent sequences:  A194902 A194903 A194904 * A194906 A194907 A194908

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 05 2011

STATUS

approved

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Last modified December 20 15:01 EST 2014. Contains 252266 sequences.