# The Powers of $$32$$!

One day for no apparent reason, Brilli the ant decides to add up different non-negative powers of $$32$$ and begins to write them down in ascending order. The first few terms of her sequence look like this:

$1, 32, 33, 1024, 1025, 1056, 1057, 32768, 32769, 32800, 32801...$

If $$35467067393$$ is the $$N^{\text{th}}$$ term of this sequence, what is $$N$$?

Details and assumptions:

A term can be the sum of more than two different powers of $$32$$. For example: $$32801=32^3+32^1+32^0$$.

A term can be the "sum" of one number. For example: $$1024=32^2$$ is a term of this sequence.

A term, however, can't be the "sum" of zero numbers. In other words, $$0$$ isn't in this sequence.

A term also has to be the sum of distinct numbers. That means $$65=32^1+32^1+32^0$$ is not in the sequence.

This problem was inspired by a problem posed in the BdMO-2013 divisional round.

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