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A194968 Fractalization of (1+[n/r]), where [ ]=floor, r=(1+sqrt(5))/2 (the golden ratio), and n>=1.

%I A194968 #5 Mar 30 2012 18:57:44
%S A194968 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 A194968 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 A194968 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 A194968 Fractalization of (1+[n/r]), where [ ]=floor, r=(1+sqrt(5))/2 (the golden ratio), and n>=1.
%C A194968 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  The sequence (1+[n/r]) is A019446.
%t A194968 r = GoldenRatio; p[n_] := 1 + Floor[n/r]
%t A194968 Table[p[n], {n, 1, 90}]  (* A019446 *)
%t A194968 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194968 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194968 f[20]  (* A194968 *)
%t A194968 row[n_] := Position[f[30], n];
%t A194968 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194968 v[n_, k_] := Part[row[n], k];
%t A194968 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194968 {k, 1, n}]]  (* A194969 *)
%t A194968 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194968 {n, 1, 80}]]  (* A194970 *)
%Y A194968 Cf. A194959, A019446, A194969, A194970.
%K A194968 nonn
%O A194968 1,3
%A A194968 _Clark Kimberling_, Sep 07 2011