Difference between revisions of "2013 USAJMO Problems/Problem 4"
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| − | Let be the number of ways to write as a sum of powers of , where we keep track of the order of the summation. For example, because can be written as , , , , , and . Find the smallest greater than for which is odd. | + | Let <math>f(n)</math> be the number of ways to write <math>n</math> as a sum of powers of <math>2</math>, where we keep track of the order of the summation. For example, <math>f(4)=6</math> because <math>4</math> can be written as <math>4</math>, <math>2+2</math>, <math>2+1+1</math>, <math>1+2+1</math>, <math>1+1+2</math>, and <math>1+1+1+1</math>. Find the smallest <math>n</math> greater than <math>2013</math> for which <math>f(n)</math> is odd.[/ |
Revision as of 19:52, 11 May 2013
Let 
be the number of ways to write 
as a sum of powers of 
, where we keep track of the order of the summation. For example, 
because 
can be written as , 
, 
, 
, 
, and 
. Find the smallest greater than 
for which is odd.[/
