Difference between revisions of "2007 OIM Problems/Problem 1"
(Created page with "== Problem == Given a positive integer <math>m</math>, the sequence {<math>a_n</math>} is defined as follows: <math></math>a_1=\frac{m}{2},\;a_{n+1}=a_n\left\lceil a_n \right...") |
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Given a positive integer <math>m</math>, the sequence {<math>a_n</math>} is defined as follows: | Given a positive integer <math>m</math>, the sequence {<math>a_n</math>} is defined as follows: | ||
| − | < | + | <cmath>a_1=\frac{m}{2},\;a_{n+1}=a_n\left\lceil a_n \right\rceil,\; \text{ if }n\ge 1</cmath> |
| − | Find all values of < | + | Find all values of <math>m</math> for which <math>a_{2007}</math> is the first integer that appears in the succession. |
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Latest revision as of 16:40, 14 December 2023
Problem
Given a positive integer 
, the sequence {
} is defined as follows:
![\[a_1=\frac{m}{2},\;a_{n+1}=a_n\left\lceil a_n \right\rceil,\; \text{ if }n\ge 1\]](http://latex.artofproblemsolving.com/7/7/9/77969268eec3e8ee3f7fe0cb56d7268d46b06bdc.png)
Find all values of for which 
is the first integer that appears in the succession.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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