A195097 - OEIS

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A195097

Fractalization of (1+[3n/4]), where [ ] = floor.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (1+[3n/4]) is a subsequence ofy A037915.

LINKS

Table of n, a(n) for n=1..94.

MATHEMATICA

r = 3/4; p[n_] := 1 + Floor[n*r] (* A037915 *)

Table[p[n], {n, 1, 90}]

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

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

f[20] (* A195097 *)

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

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

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

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