A195113 Fractalization of the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.

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

Author

Clark Kimberling, Sep 09 2011

Keywords

• nonn

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.

Crossrefs

Cf. A194959, A002260, A195114, A195115.

Programs

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 *)