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A194973
Fractalization of (A053737(n+4)), n>=0.
3
1, 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, 4, 1, 5, 9, 6, 7, 8, 2, 3, 4, 1, 5, 9, 10, 6, 7, 8, 2, 3, 4, 1, 5, 9, 10, 11, 6, 7, 8, 2, 3, 4, 1, 5, 9, 10, 11, 12, 6, 7, 8, 2, 3, 4, 1, 5, 9, 13, 10, 11, 12, 6, 7, 8, 2, 3, 4, 1, 5, 9
OFFSET
1,3
COMMENTS
See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (A053737(n+4)), n>=0 is formed by concatenating 4-tuples of the form (n,n+1,n+2, n+3) for n>=1: 1,2,3,4,2,3,4,5,3,4,5,6,...
MATHEMATICA
p[n_] := Floor[(n + 3)/4] + Mod[n - 1, 4]
Table[p[n], {n, 1, 90}] (* A053737(n+4), n>=0 *)
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] (* A194973 *)
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},
{k, 1, n}]] (* A194974 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A194975 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 07 2011
STATUS
approved