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 A194965 #5 Mar 30 2012 18:57:44 %S A194965 1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1,6,2,3,4,5,1,6,7,2,3,4,5,1,6,7,8,2,3, %T A194965 4,5,1,6,7,8,9,2,3,4,5,1,6,7,8,9,10,2,3,4,5,1,6,11,7,8,9,10,2,3,4,5,1, %U A194965 6,11,12,7,8,9,10,2,3,4,5,1,6,11,12,13,7,8,9,10,2,3,4,5,1,6,11 %N A194965 Fractalization of (A053824(n+5)), n>=0. %C A194965 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (A053724(n+5)), n>=0 is formed by concatenating 5-tuples of the form (n,n+1,n+2, n+3,n+4) for n>=1: 1,2,3,4,5,2,3,4,5,6,3,4,5,6,7,... %t A194965 p[n_] := Floor[(n + 4)/5] + Mod[n - 1, 5] %t A194965 Table[p[n], {n, 1, 90}] (* A053824(n+5), n>=0 *) %t A194965 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]] %t A194965 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]] %t A194965 f[20] (* A194965 *) %t A194965 row[n_] := Position[f[30], n]; %t A194965 u = TableForm[Table[row[n], {n, 1, 5}]] %t A194965 v[n_, k_] := Part[row[n], k]; %t A194965 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, %t A194965 {k, 1, n}]] (* A194966 *) %t A194965 q[n_] := Position[w, n]; Flatten[ %t A194965 Table[q[n], {n, 1, 80}]] (* A194967 *) %Y A194965 Cf. A194959, A194965, A194966, A194967. %K A194965 nonn %O A194965 1,3 %A A194965 _Clark Kimberling_, Sep 07 2011