A194066 - OEIS

%I #12 Dec 26 2023 10:23:48

%S 1,1,2,1,2,1,2,3,1,2,3,4,1,2,3,4,1,2,3,4,5,1,2,3,4,5,6,1,2,3,4,5,6,1,

%T 2,3,4,5,6,7,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,9,1,2,3,

%U 4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,11,1

%N Natural fractal sequence of A087483.

%C See A194029 for definitions of natural fractal sequence and natural interspersion.

%t z = 70;

%t c[k_] := 1 + Floor[(1/3) k^2];

%t c = Table[c[k], {k, 1, z}]  (* A087483 *)

%t f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]

%t f = Table[f[n], {n, 1, 300}]   (* A194066 *)

%t r[n_] := Flatten[Position[f, n]]

%t t[n_, k_] := r[n][[k]]

%t TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]

%t p = Flatten[Table[t[k, n - k + 1], {n, 1, 14}, {k, 1, n}]] (* A194067 *)

%t q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194068 *)

%Y Cf. A194029, A194067, A087483.

%K nonn

%O 1,3

%A _Clark Kimberling_, Aug 14 2011