A195082 - OEIS

%I #6 Mar 30 2012 18:57:44

%S 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,

%T 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,

%U 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

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

%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  The sequence (1+[2n/3]) is essentially A004396.

%t r = 2/3; p[n_] := 1 + Floor[n*r]

%t Table[p[n], {n, 1, 90}]  (* ess A004396 *)

%t g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]

%t f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]

%t f[20] (* A195082 *)

%t row[n_] := Position[f[30], n];

%t u = TableForm[Table[row[n], {n, 1, 5}]]

%t v[n_, k_] := Part[row[n], k];

%t w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, ]

%t {k, 1, n}]] (* A195083 *)

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

%t {n, 1, 80}]] (* A195096 *)

%Y Cf. A004396, A195083, A195096.

%K nonn

%O 1,3

%A _Clark Kimberling_, Sep 08 2011