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).

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

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: A357457 A194902 A194874 * A054065 A194868 A304574

Adjacent sequences: A194832 A194833 A194834 * A194836 A194837 A194838

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 03 2011

Status

approved