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A195073 Fractalization of (n-[n/sqrt(3)]), where [ ]=floor.

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%I A195073 #6 Mar 30 2012 18:57:44
%S A195073 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 A195073 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 A195073 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 A195073 Fractalization of (n-[n/sqrt(3)]), where [ ]=floor.
%C A195073 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  The sequence (n-[n/sqrt(3)]) is A195072.
%t A195073 r = Sqrt[3]; p[n_] := n - Floor[n/r]
%t A195073 Table[p[n], {n, 1, 90}]   (* A195072 *)
%t A195073 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195073 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195073 f[20]   (* A195073 *)
%t A195073 row[n_] := Position[f[30], n];
%t A195073 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195073 v[n_, k_] := Part[row[n], k];
%t A195073 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A195073 {k, 1, n}]]    (* A195074 *)
%t A195073 q[n_] := Position[w, n]; Flatten[
%t A195073 Table[q[n], {n, 1, 80}]]   (* A195075 *)
%Y A195073 Cf. A195072, A194974, A195075.
%K A195073 nonn
%O A195073 1,2
%A A195073 _Clark Kimberling_, Sep 08 2011