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A195183
Fractalization of the prime marker sequence A089026.
3
1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 5, 6, 4, 1, 2, 3, 5, 6, 4, 1, 2, 3, 5, 7, 8, 6, 4, 1, 2, 3, 5, 7, 9, 8, 6, 4, 1, 2, 3, 5, 7, 10, 9, 8, 6, 4, 1, 2, 3, 5, 7, 10, 9, 8, 6, 4, 1, 2, 3, 5, 7, 11, 12, 10, 9, 8, 6, 4, 1, 2, 3, 5, 7, 11, 12, 10, 9, 8, 6, 4, 1, 2, 3, 5, 7, 11, 13, 14, 12
OFFSET
1,3
COMMENTS
See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. (The prime marker sequence A089026 is defined by p(n)=n if n is prime and p(n)=1 otherwise.)
LINKS
MATHEMATICA
Table[p[n], {n, 1, 90}] (* A089026 *)
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] (* A195183 *)
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}]] (* A195184 *)
q[n_] := Position[w, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A195185 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 10 2011
STATUS
approved