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A194961 Fractalization of A194960.

%I A194961 #11 Oct 23 2022 23:12:14
%S A194961 1,1,2,1,2,3,1,4,2,3,1,4,5,2,3,1,4,5,6,2,3,1,4,7,5,6,2,3,1,4,7,8,5,6,
%T A194961 2,3,1,4,7,8,9,5,6,2,3,1,4,7,10,8,9,5,6,2,3,1,4,7,10,11,8,9,5,6,2,3,1,
%U A194961 4,7,10,11,12,8,9,5,6,2,3,1,4,7,10,13,11,12,8,9,5,6,2,3,1,4,7
%N A194961 Fractalization of A194960.
%C A194961 See A194959 for a discussion of fractalization.
%H A194961 G. C. Greubel, <a href="/A194961/b194961.txt">Table of n, a(n) for n = 1..5000</a>
%t A194961 p[n_] := Floor[(n + 2)/3] + Mod[n - 1, 3]
%t A194961 Table[p[n], {n, 1, 90}]  (* A194960 *)
%t A194961 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194961 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194961 f[20]  (* A194961 *)
%t A194961 row[n_] := Position[f[30], n];
%t A194961 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194961 v[n_, k_] := Part[row[n], k];
%t A194961 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]  (* A194962 *)
%t A194961 q[n_] := Position[w, n]; Flatten[
%t A194961 Table[q[n], {n, 1, 80}]]  (* A194963 *)
%Y A194961 Cf. A194959, A194960, A194962, A194963.
%K A194961 nonn
%O A194961 1,3
%A A194961 _Clark Kimberling_, Sep 06 2011