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Omni-MATH / Let f(n) be the number of ways to write n as a sum of powers of 2 , where we keep track of the order of the summation. For example, f(4)=6 because 4 can be written as 4 , 2+2 , …

Problem

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problem

Let

f(n)

be the number of ways to write

n

as a sum of powers of

2

, where we keep track of the order of the summation. For example,

f(4)=6

because

4

can be written as

4

2+2

2+1+1

1+2+1

1+1+2

, and

1+1+1+1

. Find the smallest

n

greater than

2013

for which

f(n)

is odd.

Plain-text mathematical notation (without MathML)

Let f(n) be the number of ways to write n as a sum of powers of 2 , where we keep track of the order of the summation.  For example, f(4)=6 because 4 can be written as 4 , 2+2 , 2+1+1 , 1+2+1 , 1+1+2 , and 1+1+1+1 .  Find the smallest n greater than 2013 for which f(n) is odd.

Original LaTeX notation

Let $f(n)$ be the number of ways to write $n$ as a sum of powers of $2$ , where we keep track of the order of the summation.  For example, $f(4)=6$ because $4$ can be written as $4$ , $2+2$ , $2+1+1$ , $1+2+1$ , $1+1+2$ , and $1+1+1+1$ .  Find the smallest $n$ greater than $2013$ for which $f(n)$ is odd.

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task_id: cec45f07-460f-5938-9cd9-975cfd87c125
task_key: test--cec45f07-460f-5938-9cd9-975cfd87c125
task_revision_id: 4
config / split: / test

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