Timeline for Writing integers as a product of as few elements of $\{\frac21, \frac32, \frac43, \frac54, \ldots\}$ as possible

9 events

when toggle format	what		by	license	comment
Jun 15, 2020 at 7:27	history	edited	CommunityBot		Commonmark migration
Apr 23, 2018 at 16:35	comment	added	Lucia		Doesn't answer your question, but one can show that $f(x)$ is not $\log_2 x + O(1)$. This also suggests that $f(xy)$ is not $f(x) + f(y) -O(1)$.
Apr 23, 2018 at 4:54	comment	added	George Shakan		One idea is to use a lower bound sieve to show that $kp^{\alpha}-1$ is an almost prime for a small choice of $k$ and then iterate.
Apr 22, 2018 at 10:33	comment	added	user133281		Added to the list of observations.
Apr 22, 2018 at 10:33	history	edited	user133281	CC BY-SA 3.0	added 197 characters in body
Apr 22, 2018 at 10:24	comment	added	Chris Wuthrich		Maybe it is worth adding to the question the result from the partial answer on math.stackexchange. For instance $f(x)\leq 2\log_2(x)$.
Apr 22, 2018 at 7:47	comment	added	Greg Martin		The following subquestion also seems interesting: how does the greedy algorithm perform in terms of finding a representation with few terms? I note that the first and last examples given are the result of the greedy algorithm.
Apr 22, 2018 at 7:37	review	First posts
Apr 22, 2018 at 7:54
Apr 22, 2018 at 7:34	history	asked	user133281	CC BY-SA 3.0