MathDB

A positive integer

n

is tripariable if it is possible to partition the set

\{1, 2, \dots, n\}

into disjoint pairs such that the sum of two elements in each pair is a power of

3

. For example

6

is tripariable because

\{1, 2, \dots, n\}=\{1,2\}\cup\{3,6\}\cup\{4,5\}

and 1+2=3^1, 3+6 = 3^2 \text{and} 4+5=3^2 are all powers of 3.
How many positive integers less than or equal to 2024 are tripariable?

A2