

A195110


Fractalization of the fractal sequence A002260. Interspersion fractally induced by A002260.


4



1, 2, 1, 2, 3, 1, 4, 2, 3, 1, 4, 5, 2, 3, 1, 4, 5, 6, 2, 3, 1, 7, 4, 5, 6, 2, 3, 1, 7, 8, 4, 5, 6, 2, 3, 1, 7, 8, 9, 4, 5, 6, 2, 3, 1, 7, 8, 9, 10, 4, 5, 6, 2, 3, 1, 11, 7, 8, 9, 10, 4, 5, 6, 2, 3, 1, 11, 12, 7, 8, 9, 10, 4, 5, 6, 2, 3, 1, 11, 12, 13, 7, 8, 9, 10, 4, 5, 6, 2, 3, 1, 11, 12
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OFFSET

1,2


COMMENTS

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence A002260 is the fractal sequence obtained by concatenating the segments 1; 12; 123; 1234; 12345;...


LINKS

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


MATHEMATICA

j[n_] := Table[k, {k, 1, n}]; t[1] = j[1];
t[n_] := Join[t[n  1], j[n]] (* A002260 *)
t[12]
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] (* A195110 *)
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}]] (* A195111 *)
q[n_] := Position[w, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A195112 *)


CROSSREFS

Cf. A194959, A002260, A195111, A195112.
Sequence in context: A021475 A132224 A194961 * A167198 A295540 A133299
Adjacent sequences: A195107 A195108 A195109 * A195111 A195112 A195113


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 09 2011


STATUS

approved



