A195097 Fractalization of (1+[3n/4]), where [ ] = floor.

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

Offset: 1

Author

Clark Kimberling, Sep 08 2011

Keywords

• nonn

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (1+[3n/4]) is a subsequence ofy A037915.

Crossrefs

Cf. A194959, A002265, A195098, A195099.

Programs

Mathematica

r = 3/4; p[n_] := 1 + Floor[n*r] (* A037915 *)
Table[p[n], {n, 1, 90}]
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]    (* A195097 *)
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}]](* A195098 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]](* A195099 *)