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%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
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