%I #5 Mar 30 2012 18:57:44

%S 1,2,1,2,3,1,2,4,3,1,2,4,5,3,1,2,4,6,5,3,1,2,4,6,7,5,3,1,2,4,6,8,7,5,

%T 3,1,2,4,6,8,9,7,5,3,1,2,4,6,8,10,9,7,5,3,1,2,4,6,8,11,10,9,7,5,3,1,2,

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

%N Fractalization of (1+[n/sqrt(5)]), where [ ]=floor.

%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (1+[n/sqrt(5)]) is A194964.

%t r = Sqrt[5]; p[n_] := 1 + Floor[n/r]

%t Table[p[n], {n, 1, 90}] (* A194964 *)

%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] (* A194983 *)

%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}]] (* A194984 *)

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

%t {n, 1, 80}]] (* A194985 *)

%Y Cf. A194959, A194983, A194984, A194985.

%K nonn

%O 1,2

%A _Clark Kimberling_, Sep 07 2011