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%I #6 Mar 30 2012 18:57:44
%S 1,2,1,2,3,1,2,4,3,1,2,4,5,3,1,2,4,6,5,3,1,2,4,7,6,5,3,1,2,4,7,8,6,5,
%T 3,1,2,4,7,9,8,6,5,3,1,2,4,7,9,10,8,6,5,3,1,2,4,7,9,11,10,8,6,5,3,1,2,
%U 4,7,9,11,12,10,8,6,5,3,1,2,4,7,9,11,13,12,10,8,6,5,3,1,2,4,7,9
%N Fractalization of (n-[n/sqrt(3)]), where [ ]=floor.
%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (n-[n/sqrt(3)]) is A195072.
%t r = Sqrt[3]; p[n_] := n - Floor[n/r]
%t Table[p[n], {n, 1, 90}] (* A195072 *)
%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] (* A195073 *)
%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}]] (* A195074 *)
%t q[n_] := Position[w, n]; Flatten[
%t Table[q[n], {n, 1, 80}]] (* A195075 *)
%Y Cf. A195072, A194974, A195075.
%K nonn
%O 1,2
%A _Clark Kimberling_, Sep 08 2011
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