login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A194838 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(3). 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, 11, 7, 3, 10, 6, 2, 9, 5, 1, 8, 4, 11, 7, 3, 10, 6, 2, 9, 5, 1, 12, 8, 4, 11, 7, 3, 10, 6, 2, 13, 9, 5, 1, 12, 8, 4, 11, 7, 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:

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 = Sqrt[3];

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

f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]  (* A194838 *)

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}]]  (* A194839 *)

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

Table[q[n], {n, 1, 80}]]  (* A194840 *)

CROSSREFS

Cf. A194832, A194839, A194840.

Sequence in context: A131756 A212620 A194859 * A085014 A082074 A132283

Adjacent sequences:  A194835 A194836 A194837 * A194839 A194840 A194841

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 03 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 27 04:58 EDT 2021. Contains 346305 sequences. (Running on oeis4.)