A194976 Fractalization of (1+[n/sqrt(2)]), 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, 9, 10, 6, 3, 1, 2, 4, 5, 7, 8, 9, 11, 10, 6, 3, 1, 2, 4, 5, 7, 8, 9, 11, 12, 10, 6, 3, 1, 2, 4, 5, 7, 8, 9, 11, 12, 13, 10, 6, 3, 1, 2, 4

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(2)]) is A049474.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..11325

Crossrefs

Cf. A194959, A049474, A194977, A194978.

Programs

Mathematica

r = Sqrt[2]; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A049474 *)
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] (* A194976 *)
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}]] (* A194977 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A194978 *)