A195183 Fractalization of the prime marker sequence A089026.

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

Author

Clark Kimberling, Sep 10 2011

Keywords

• nonn

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

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A194959, A089026, A195184, A195185.

Programs

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 *)