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

1,2

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