Intended for: February 2, 2012
Timetable
 First draft entered by Alonso del Arte on November 3, 2011 ✓
 Draft reviewed by Daniel Forgues on January 29, 2017 ✓ (presentation review only)
 Draft to be approved by January 2, 2012
Yesterday's SOTD * Tomorrow's SOTD
The line below marks the end of the <noinclude> ... </noinclude> section.
A196244: Number of distinct values taken by
where
(with
’s and parentheses inserted in all possible ways).

{ 1, 1, 2, 4, 9, 20, 47, ... }
In the case of say,
, we’re considering the expressions
 ${\begin{array}{l}\displaystyle {{\frac {1}{2}}^{\left({\frac {1}{2}}^{\left({\frac {1}{2}}^{\frac {1}{2}}\right)}\right)},}\end{array}}$${\begin{array}{l}\displaystyle {{\frac {1}{2}}^{\left({\left({\frac {1}{2}}^{\frac {1}{2}}\right)}^{\frac {1}{2}}\right)},}\end{array}}$${\begin{array}{l}\displaystyle {{\left({\frac {1}{2}}^{\frac {1}{2}}\right)}^{\left({\frac {1}{2}}^{\frac {1}{2}}\right)},}\end{array}}$${\begin{array}{l}\displaystyle {{\left({\frac {1}{2}}^{\left({\frac {1}{2}}^{\frac {1}{2}}\right)}\right)}^{\frac {1}{2}},}\end{array}}$${\begin{array}{l}\displaystyle {{\left({\left({\frac {1}{2}}^{\frac {1}{2}}\right)}^{\frac {1}{2}}\right)}^{\frac {1}{2}},}\end{array}}$
and whether or not these expressions result in distinct values or not.