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Fractalization of (A053824(n+5)), n>=0.
3

%I #5 Mar 30 2012 18:57:44

%S 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 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 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 Fractalization of (A053824(n+5)), n>=0.

%C 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 p[n_] := Floor[(n + 4)/5] + Mod[n - 1, 5]

%t Table[p[n], {n, 1, 90}] (* A053824(n+5), n>=0 *)

%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] (* A194965 *)

%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}]] (* A194966 *)

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

%t Table[q[n], {n, 1, 80}]] (* A194967 *)

%Y Cf. A194959, A194965, A194966, A194967.

%K nonn

%O 1,3

%A _Clark Kimberling_, Sep 07 2011