Template:Sequence of the Day for February 2

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

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A196244: Number of distinct values taken by

r  r  ⋰  r

where

r = 1  2

(with

n

r

’s and parentheses inserted in all possible ways).

{ 1, 1, 2, 4, 9, 20, 47, ... }

In the case of say,

n = 4

, 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.