A194877 - OEIS

A194877

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(8).

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

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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

4 3 2 1

5 4 3 2 1

5 4 3 2 1 6

5 4 3 2 7 1 6

5 4 3 8 2 7 1 6

5 4 9 3 8 2 7 1 6

MATHEMATICA

r = Sqrt[8];

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

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

Sort[t[n], Less]], {n, 1, 20}]] (* A194877 *)

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}]] (* A194878 *)

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

{n, 1, 80}]] (* A194879 *)

CROSSREFS

Cf. A194832, A194878, A194879.

Sequence in context: A088643 A361642 A226620 * A102482 A194908 A004736

Adjacent sequences: A194874 A194875 A194876 * A194878 A194879 A194880

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 04 2011

STATUS

approved