A194921 - OEIS

%I #10 Nov 18 2017 17:53:52

%S 1,2,1,3,2,1,3,4,2,1,3,5,4,2,1,3,6,5,4,2,1,3,6,7,5,4,2,1,3,6,8,7,5,4,

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

%U 6,10,12,11,9,8,7,5,4,2,1,3,6,10,13,12,11,9,8,7,5,4,2,1,3,6,10

%N Fractalization of (n - [n/sqrt(2)]), where [ ]=floor.

%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (n-[n/sqrt(2)]) is A194920.

%H G. C. Greubel, <a href="/A194921/b194921.txt">Table of n, a(n) for n = 1..5050</a>

%t r = Sqrt[2]; p[n_] := n - Floor[n/r]

%t Table[p[n], {n, 1, 90}]  (* A194920 *)

%t g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]

%t f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]

%t f[20]  (* A194921 *)

%t row[n_] := Position[f[30], n];

%t u = TableForm[Table[row[n], {n, 1, 5}]]

%t v[n_, k_] := Part[row[n], k];

%t w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},

%t {k, 1, n}]]  (* A194922 *)

%t q[n_] := Position[w, n]; Flatten[Table[q[n],

%t {n, 1, 80}]]   (* A195071 *)

%Y Cf. A194920, A194922, A195071.

%K nonn

%O 1,2

%A _Clark Kimberling_, Sep 08 2011