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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 16:09 EDT 2018. Contains 316323 sequences. (Running on oeis4.)