_Clark Kimberling (ck6(AT)evansville.edu), _, Sep 08 2011

proposed

approved

editing

proposed

{k, 1, n}]] (* A195074 *)

Cf. A194972, A195072, A194974, A195075.

allocated for Clark Kimberling

Fractalization of (n-[n/sqrt(3)]), where [ ]=floor.

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

1,2

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (n-[n/sqrt(3)]) is A195072.

r = Sqrt[3]; p[n_] := n - Floor[n/r]

Table[p[n], {n, 1, 90}] (* A195072 *)

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] (* A195073 *)

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}]] (* A195074 *)

q[n_] := Position[w, n]; Flatten[

Table[q[n], {n, 1, 80}]] (* A195075 *)

Cf. A194972, A194974, A195075.

allocated

nonn

Clark Kimberling (ck6(AT)evansville.edu), Sep 08 2011

approved

editing

allocated for Clark Kimberling

allocated

approved