A194859 - OEIS

A194859

Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {e}, {2e}, ..., {ne}.

1, 2, 1, 3, 2, 1, 3, 2, 1, 4, 3, 2, 5, 1, 4, 3, 6, 2, 5, 1, 4, 7, 3, 6, 2, 5, 1, 4, 7, 3, 6, 2, 5, 1, 8, 4, 7, 3, 6, 2, 9, 5, 1, 8, 4, 7, 3, 10, 6, 2, 9, 5, 1, 8, 4, 7, 3, 10, 6, 2, 9, 5, 1, 8, 4, 11, 7, 3, 10, 6, 2, 9, 5, 12, 1, 8, 4, 11, 7, 3, 10, 6, 13, 2, 9, 5, 12, 1, 8, 4, 11, 7, 14, 3

(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:

2 1

3 2 1

3 2 1 4

3 2 5 1 4

3 6 2 5 1 4

7 3 6 2 5 1 4

7 3 6 2 5 1 8 4

7 3 6 2 9 5 1 8 4

MATHEMATICA

r = E;

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

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

Sort[t[n], Less]], {n, 1, 20}]] (* A194859 *)

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}]] (* A194860 *)

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

{n, 1, 80}]] (* A194861 *)

CROSSREFS

Cf. A194832, A194860, A194861.

Sequence in context: A174737 A131756 A212620 * A194838 A085014 A082074

Adjacent sequences: A194856 A194857 A194858 * A194860 A194861 A194862

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 04 2011

STATUS

approved