A194980 Fractalization of (1+[n/sqrt(3)]), where [ ]=floor.

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

Offset: 1

Author

Clark Kimberling, Sep 07 2011

Keywords

• nonn

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (1+[n/sqrt(3)]) is A194979.

Crossrefs

Cf. A194959, A194879, A194981, A194982.

Programs

Mathematica

r = Sqrt[3]; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194979 = 1+ A097337 *)
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] (* A194980 *)
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}]]  (* A194981 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194982 *)