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Fractalization of the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.
3

%I #9 Jul 24 2014 11:23:40

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

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

%U 10,11,12,5,6,7,8,2,3,4,1,9,10,11,12,13,5,6,7,8,2,3,4,1,14,9,10

%N Fractalization of the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.

%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence p; for the present case, p is the concatenation of the segments 1, 123,1234,12345,123456,..., so that p is obtained from A002260 by deleting the segment 12.

%t j[n_] := Table[k, {k, 1, n}];

%t t[1] = j[1]; t[2] = j[1];

%t t[n_] := Join[t[n - 1], j[n]] (* A002260; initial 1,1,2 repl by 1 *)

%t t[12]

%t p[n_] := t[20][[n]]

%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] (* A195113 *)

%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}]] (* A195114 *)

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

%t {n, 1, 80}]] (* A195115 *)

%Y Cf. A194959, A002260, A195114, A195115.

%K nonn

%O 1,2

%A _Clark Kimberling_, Sep 09 2011