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A194835 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=-sqrt(2). 5
1, 2, 1, 2, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 5, 2, 4, 6, 1, 3, 5, 7, 2, 4, 6, 1, 3, 5, 7, 2, 4, 6, 1, 8, 3, 5, 7, 2, 9, 4, 6, 1, 8, 3, 5, 7, 2, 9, 4, 6, 1, 8, 3, 10, 5, 7, 2, 9, 4, 11, 6, 1, 8, 3, 10, 5, 12, 7, 2, 9, 4, 11, 6, 1, 8, 3, 10, 5, 12, 7, 2, 9, 4, 11, 6, 1, 13, 8, 3, 10, 5, 12, 7, 2 (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

2 1 3

2 4 1 3

2 4 1 3 5

2 4 6 1 3 5

7 2 4 6 1 3 5

7 2 4 6 1 8 3 5

7 2 9 4 6 1 8 3 5

MATHEMATICA

r = -Sqrt[2];

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

f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]  (* A194835 *)

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}]] (* A194836 *)

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

{n, 1, 80}]]  (* A194837 *)

CROSSREFS

Cf. A194832, A194836, A194837.

Sequence in context: A259771 A194902 A194874 * A054065 A194868 A304574

Adjacent sequences:  A194832 A194833 A194834 * A194836 A194837 A194838

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 03 2011

STATUS

approved

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Last modified June 4 05:19 EDT 2020. Contains 334815 sequences. (Running on oeis4.)