This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A195082 #10 Jun 26 2025 07:30:36
%S A195082 1,1,2,1,2,3,1,2,4,3,1,2,4,5,3,1,2,4,5,6,3,1,2,4,5,7,6,3,1,2,4,5,7,8,
%T A195082 6,3,1,2,4,5,7,8,9,6,3,1,2,4,5,7,8,10,9,6,3,1,2,4,5,7,8,10,11,9,6,3,1,
%U A195082 2,4,5,7,8,10,11,12,9,6,3,1,2,4,5,7,8,10,11,13,12,9,6,3,1,2,4
%N A195082 Fractalization of (1+[2*n/3]), where [ ] = floor.
%C A195082 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (1+[2*n/3]) is essentially A004396.
%t A195082 r = 2/3; p[n_] := 1 + Floor[n*r]
%t A195082 Table[p[n], {n, 1, 90}] (* ess A004396 *)
%t A195082 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195082 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195082 f[20] (* A195082 *)
%t A195082 row[n_] := Position[f[30], n];
%t A195082 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195082 v[n_, k_] := Part[row[n], k];
%t A195082 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, {k, 1, n}]] (* A195083 *)
%t A195082 q[n_] := Position[w, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A195096 *)
%Y A195082 Cf. A004396, A195083, A195096.
%K A195082 nonn
%O A195082 1,3
%A A195082 _Clark Kimberling_, Sep 08 2011