A195082 Fractalization of (1+[2*n/3]), where [ ] = floor.

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

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+[2*n/3]) is essentially A004396.

Crossrefs

Cf. A004396, A195083, A195096.

Programs

Mathematica

r = 2/3; p[n_] := 1 + Floor[n*r]
Table[p[n], {n, 1, 90}]  (* ess A004396 *)
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] (* A195082 *)
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}]] (* A195083 *)
q[n_] := Position[w, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A195096 *)