A195107 Fractalization of the fractal sequence A004736. Interspersion fractally induced by A004736.

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

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. The sequence A004736 is the fractal sequence obtained by concatenating the segments 1; 2,1; 3,2,1; 4,3,2,1;...

Crossrefs

Cf. A194959, A004736, A195108, A195109.

Programs

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 *)