Given a function f: N->N and non-negative integer n, output integer k s.t. f(f(...f(n)..)) (repeat k times) = 0, or some non-natural number if no k exist.
You can assume f is bounded, i.e. there's some number M s.t. for each n, f(n)<M.
code-golf
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Task
Output the sequence that precisely consists of the following integers in increasing order:
the 2nd and higher powers of 10 (\$10^i\$ where \$i \ge 2\$),
the squares of powers of 10 times 2 or 3 (\$(2\times 10^i)^2\$ and \$(3\times 10^i)^2\$ where \$i \ge 1\$), and
the cubes of powers of 10 ...
In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but can also include disconnected sets of edges, called a compound polygon. For example, a regular pentagram, {5/2}, has 5 sides, and the regular hexagram, {6/2} or 2{3}, has 6 sides divided into two triangles.
A regular polygram {p/q} can either be in a set of regular star polygons (for gcd(p,q) =β1, q >β1) or in a set of regular polygon compounds (if gcd(p,q) >β1).
== Etymology ==
The polygram names combine a numeral prefix, such as penta-, with the Greek suffix...
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