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 A194973 #6 Mar 30 2012 18:57:44 %S A194973 1,1,2,1,2,3,1,2,3,4,1,5,2,3,4,1,5,6,2,3,4,1,5,6,7,2,3,4,1,5,6,7,8,2, %T A194973 3,4,1,5,9,6,7,8,2,3,4,1,5,9,10,6,7,8,2,3,4,1,5,9,10,11,6,7,8,2,3,4,1, %U A194973 5,9,10,11,12,6,7,8,2,3,4,1,5,9,13,10,11,12,6,7,8,2,3,4,1,5,9 %N A194973 Fractalization of (A053737(n+4)), n>=0. %C A194973 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (A053737(n+4)), n>=0 is formed by concatenating 4-tuples of the form (n,n+1,n+2, n+3) for n>=1: 1,2,3,4,2,3,4,5,3,4,5,6,... %t A194973 p[n_] := Floor[(n + 3)/4] + Mod[n - 1, 4] %t A194973 Table[p[n], {n, 1, 90}] (* A053737(n+4), n>=0 *) %t A194973 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]] %t A194973 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]] %t A194973 f[20] (* A194973 *) %t A194973 row[n_] := Position[f[30], n]; %t A194973 u = TableForm[Table[row[n], {n, 1, 5}]] %t A194973 v[n_, k_] := Part[row[n], k]; %t A194973 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, %t A194973 {k, 1, n}]] (* A194974 *) %t A194973 q[n_] := Position[w, n]; Flatten[Table[q[n], %t A194973 {n, 1, 80}]] (* A194975 *) %Y A194973 Cf. A194959, A194974, A194975. %K A194973 nonn %O A194973 1,3 %A A194973 _Clark Kimberling_, Sep 07 2011