A194914 Fractalization of (1+[n/sqrt(8)]), where [ ]=floor.

1, 2, 1, 2, 3, 1, 2, 4, 3, 1, 2, 5, 4, 3, 1, 2, 5, 6, 4, 3, 1, 2, 5, 7, 6, 4, 3, 1, 2, 5, 8, 7, 6, 4, 3, 1, 2, 5, 8, 9, 7, 6, 4, 3, 1, 2, 5, 8, 10, 9, 7, 6, 4, 3, 1, 2, 5, 8, 11, 10, 9, 7, 6, 4, 3, 1, 2, 5, 8, 11, 12, 10, 9, 7, 6, 4, 3, 1, 2, 5, 8, 11, 13, 12, 10, 9, 7, 6, 4, 3, 1, 2, 5, 8

Offset

1,2

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (1+[n/sqrt(8)]) is A194990.

Links

Table of n, a(n) for n=1..94.

Mathematica

r = Sqrt[8]; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194990  *)
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] (* A194914 *)
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}]]  (* A194915 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194916 *)

Crossrefs

Cf. A194959, A194914, A194915, A194916.

Sequence in context: A195073 A194987 A194917 * A195076 A163491 A080772

Adjacent sequences: A194911 A194912 A194913 * A194915 A194916 A194917

Keyword

nonn

Author

Clark Kimberling, Sep 08 2011

Status

approved