

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
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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



