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Omni-MATH / How many of the first 1000 positive integers can be written as the sum of…

Problem

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problem

How many of the first 1000 positive integers can be written as the sum of finitely many distinct numbers from the sequence 30,31,32,…3^{0}, 3^{1}, 3^{2}, \ldots?
Plain-text mathematical notation (without MathML)
How many of the first 1000 positive integers can be written as the sum of finitely many distinct numbers from the sequence 3⁰,3¹,3²,…?
Original LaTeX notation
How many of the first 1000 positive integers can be written as the sum of finitely many distinct numbers from the sequence $3^{0}, 3^{1}, 3^{2}, \ldots$?

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