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A194899 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(12). 4
1, 1, 2, 3, 1, 2, 3, 1, 4, 2, 5, 3, 1, 4, 2, 5, 3, 1, 6, 4, 2, 7, 5, 3, 1, 6, 4, 2, 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, 3, 1, 10, 8, 6, 4, 2, 11, 9, 7, 5, 3, 1, 10, 8, 6, 4, 2, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2, 13, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A194832 for a general discussion.

LINKS

Table of n, a(n) for n=1..91.

EXAMPLE

First nine rows:

1

1 2

3 1 2

3 1 4 2

5 3 1 4 2

5 3 1 6 4 2

7 5 3 1 6 4 2

7 5 3 1 8 6 4 2

9 7 5 3 1 8 6 4 2

MATHEMATICA

r = Sqrt[12];

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

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

Sort[t[n], Less]], {n, 1, 20}]] (* A194899 *)

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, 15},

{k, 1, n}]] (* A194900 *)

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

{n, 1, 90}]] (* A194901 *)

PROG

(PARI) row(n) = Vec(vecsort(vector(n, k, frac(k*sqrt(12))), , 1));

tabl(nn) = for (n=1, nn, print(row(n))); \\ Michel Marcus, Feb 06 2019

CROSSREFS

Cf. A194832, A194900, A194901.

Sequence in context: A195107 A054073 A194871 * A228094 A059832 A105316

Adjacent sequences: A194896 A194897 A194898 * A194900 A194901 A194902

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 05 2011

STATUS

approved

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Last modified November 28 19:17 EST 2022. Contains 358421 sequences. (Running on oeis4.)