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Omni-MATH / Find the number of positive integers j≤3²⁰¹³ such that j=∑_(k=0)^(m)((−1)^(k)⋅3^(a_(k))) for some strictly increasing sequence of nonnegative integers {a_(k)}. For example, we may …

Problem

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problem

Find the number of positive integers j≤32013j \leq 3^{2013} such that j=∑k=0m((−1)k⋅3ak)j=\sum_{k=0}^{m}\left((-1)^{k} \cdot 3^{a_{k}}\right) for some strictly increasing sequence of nonnegative integers {ak}\left\{a_{k}\right\}. For example, we may write 3=313=3^{1} and 55=30−33+3455=3^{0}-3^{3}+3^{4}, but 4 cannot be written in this form.
Plain-text mathematical notation (without MathML)
Find the number of positive integers j≤3²⁰¹³ such that j=∑_(k=0)^(m)((−1)^(k)⋅3^(a_(k))) for some strictly increasing sequence of nonnegative integers {a_(k)}. For example, we may write 3=3¹ and 55=3⁰−3³+3⁴, but 4 cannot be written in this form.
Original LaTeX notation
Find the number of positive integers $j \leq 3^{2013}$ such that $$j=\sum_{k=0}^{m}\left((-1)^{k} \cdot 3^{a_{k}}\right)$$ for some strictly increasing sequence of nonnegative integers $\left\{a_{k}\right\}$. For example, we may write $3=3^{1}$ and $55=3^{0}-3^{3}+3^{4}$, but 4 cannot be written in this form.

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Source and history

task_id
bc78fc48-0624-5e38-bab6-18cfa2eadb16
task_key
test--bc78fc48-0624-5e38-bab6-18cfa2eadb16
task_revision_id
1
config / split
/ test

Official source

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