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A195113
Fractalization of the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.
3
1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 5, 2, 3, 4, 1, 5, 6, 2, 3, 4, 1, 5, 6, 7, 2, 3, 4, 1, 5, 6, 7, 8, 2, 3, 4, 1, 9, 5, 6, 7, 8, 2, 3, 4, 1, 9, 10, 5, 6, 7, 8, 2, 3, 4, 1, 9, 10, 11, 5, 6, 7, 8, 2, 3, 4, 1, 9, 10, 11, 12, 5, 6, 7, 8, 2, 3, 4, 1, 9, 10, 11, 12, 13, 5, 6, 7, 8, 2, 3, 4, 1, 14, 9, 10
OFFSET
1,2
COMMENTS
See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence p; for the present case, p is the concatenation of the segments 1, 123,1234,12345,123456,..., so that p is obtained from A002260 by deleting the segment 12.
MATHEMATICA
j[n_] := Table[k, {k, 1, n}];
t[1] = j[1]; t[2] = j[1];
t[n_] := Join[t[n - 1], j[n]] (* A002260; initial 1, 1, 2 repl by 1 *)
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] (* A195113 *)
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}]] (* A195114 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A195115 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 09 2011
STATUS
approved