

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
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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



