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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}. 4
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
EXAMPLE
First nine rows:
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
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
Sequence in context: A174737 A131756 A212620 * A194838 A085014 A082074
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 04 2011
STATUS
approved

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Last modified July 13 17:35 EDT 2024. Contains 374284 sequences. (Running on oeis4.)