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

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

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

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

%N Fractalization of (1+[n/r]), where [ ]=floor, r=(1+sqrt(5))/2 (the golden ratio), and n>=1.

%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (1+[n/r]) is A019446.

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

%t Table[p[n], {n, 1, 90}] (* A019446 *)

%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] (* A194968 *)

%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}]] (* A194969 *)

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

%t {n, 1, 80}]] (* A194970 *)

%Y Cf. A194959, A019446, A194969, A194970.

%K nonn

%O 1,3

%A _Clark Kimberling_, Sep 07 2011