A195110 Fractalization of the fractal sequence A002260. Interspersion fractally induced by A002260.

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

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 A002260 is the fractal sequence obtained by concatenating the segments 1; 12; 123; 1234; 12345;...

Crossrefs

Cf. A194959, A002260, A195111, A195112.

Programs

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 *)