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 A194055 #15 Dec 26 2023 10:19:04 %S A194055 1,1,2,1,2,3,1,2,3,4,5,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,9,10,11,12,13, %T A194055 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1,2,3,4,5,6,7, %U A194055 8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29 %N A194055 Natural fractal sequence of A000071 (Fibonacci numbers minus 1). %C A194055 See A194029 for definitions of natural fractal sequence and natural interspersion. %t A194055 z = 50; %t A194055 c[k_] := -1 + Fibonacci[k + 2] %t A194055 c = Table[c[k], {k, 1, z}] (* A000071, F(n+2)-1 *) %t A194055 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]] %t A194055 f = Table[f[n], {n, 1, 300}] (* A194055 *) %t A194055 r[n_] := Flatten[Position[f, n]] %t A194055 t[n_, k_] := r[n][[k]] %t A194055 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]] %t A194055 p = Flatten[Table[t[k, n - k + 1], {n, 1, 11}, {k, 1, n}]] (* A194056 *) %t A194055 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]] (* A194057 *) %Y A194055 Cf. A194029, A000071, A194056, A194057. %K A194055 nonn %O A194055 1,3 %A A194055 _Clark Kimberling_, Aug 13 2011