A194917 - OEIS

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

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

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

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

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

%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  The sequence (n-[nr-n]) is A189663.

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

%t Table[p[n], {n, 1, 90}]  (* A189663 *)

%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] (*  A194917 *)

%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}]] (* A194918 *)

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

%t {n, 1, 80}]] (* A194919 *)

%Y Cf. A194959, A189663, A194918, A194919.

%K nonn

%O 1,2

%A _Clark Kimberling_, Sep 08 2011