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A054073 Fractal sequence induced by sqrt(2): for k >= 1 let p(k) be the permutation of 1,2,...,k obtained by ordering the fractional parts {h*sqrt(2)} for h=1,2,...,k; then juxtapose p(1),p(2),p(3),... 7
1, 1, 2, 3, 1, 2, 3, 1, 4, 2, 5, 3, 1, 4, 2, 5, 3, 1, 6, 4, 2, 5, 3, 1, 6, 4, 2, 7, 5, 3, 8, 1, 6, 4, 2, 7, 5, 3, 8, 1, 6, 4, 9, 2, 7, 5, 10, 3, 8, 1, 6, 4, 9, 2, 7, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8, 13, 1, 6, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A054073 generates the interspersion A054077; see A194832 and the Mathematica program.

LINKS

Table of n, a(n) for n=1..86.

G. C. Greubel, Table of n, a(n) for n = 1..5000

EXAMPLE

p(1)=(1); p(2)=(1,2); p(3)=(3,1,2); p(4)=(3,1,4,2).

When formatted as a triangle, the first 9 rows:

1

1 2

3 1 2

3 1 4 2

5 3 1 4 2

5 3 1 6 4 2

5 3 1 6 4 2 7

5 3 8 1 6 4 2 7

5 3 8 1 6 4 9 2 7

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}]] (* A054073 *)

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}]] (* A054077 *)

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

Table[q[n], {n, 1, 80}]]  (* A054076 *)

(* Clark Kimberling, Sep 03 2011 *)

CROSSREFS

Cf. A054071, A054072, A194832.

Sequence in context: A194862 A194832 A195107 * A194871 A194899 A228094

Adjacent sequences:  A054070 A054071 A054072 * A054074 A054075 A054076

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 19 00:22 EST 2022. Contains 350464 sequences. (Running on oeis4.)