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A195107 Fractalization of the fractal sequence A004736. Interspersion fractally induced by A004736. 4
1, 1, 2, 3, 1, 2, 3, 1, 4, 2, 3, 5, 1, 4, 2, 6, 3, 5, 1, 4, 2, 6, 3, 5, 7, 1, 4, 2, 6, 3, 8, 5, 7, 1, 4, 2, 6, 9, 3, 8, 5, 7, 1, 4, 2, 10, 6, 9, 3, 8, 5, 7, 1, 4, 2, 10, 6, 9, 3, 11, 8, 5, 7, 1, 4, 2, 10, 6, 9, 12, 3, 11, 8, 5, 7, 1, 4, 2, 10, 6, 13, 9, 12, 3, 11, 8, 5, 7, 1, 4, 2, 10, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  The sequence A004736 is the fractal sequence obtained by concatenating the segments 1; 2,1; 3,2,1; 4,3,2,1;...

LINKS

Table of n, a(n) for n=1..93.

MATHEMATICA

j[n_] := Table[n + 1 - k, {k, 1, n}]; t[1] = j[1];

t[n_] := Join[t[n - 1], j[n]]   (* A004736 *)

t[10]

p[n_] := t[20][[n]]

g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]

f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]

f[20] (* A195107 *)

row[n_] := Position[f[30], n];

u = TableForm[Table[row[n], {n, 1, 5}]]

v[n_, k_] := Part[row[n], k];

w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},

{k, 1, n}]] (* A195108 *)

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

{n, 1, 80}]] (* A195109 *)

CROSSREFS

Cf. A194959, A004736, A195108, A195109.

Sequence in context: A239526 A194862 A194832 * A054073 A194871 A194899

Adjacent sequences:  A195104 A195105 A195106 * A195108 A195109 A195110

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 09 2011

STATUS

approved

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Last modified June 13 03:29 EDT 2021. Contains 344980 sequences. (Running on oeis4.)