benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Define a number to be an anti-palindrome if, when written in base 3 as a_(n)a_(n−1)…a₀, then a_(i)+a_(n−i)=2 for any 0≤i≤n. Find the number of anti-palindromes less than 3¹² such t…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Define a number to be an anti-palindrome if, when written in base 3 as anan−1…a0a_{n} a_{n-1} \ldots a_{0}, then ai+an−i=2a_{i}+a_{n-i}=2 for any 0≤i≤n0 \leq i \leq n. Find the number of anti-palindromes less than 3123^{12} such that no two consecutive digits in base 3 are equal.
Plain-text mathematical notation (without MathML)
Define a number to be an anti-palindrome if, when written in base 3 as a_(n)a_(n−1)…a₀, then a_(i)+a_(n−i)=2 for any 0≤i≤n. Find the number of anti-palindromes less than 3¹² such that no two consecutive digits in base 3 are equal.
Original LaTeX notation
Define a number to be an anti-palindrome if, when written in base 3 as $a_{n} a_{n-1} \ldots a_{0}$, then $a_{i}+a_{n-i}=2$ for any $0 \leq i \leq n$. Find the number of anti-palindromes less than $3^{12}$ such that no two consecutive digits in base 3 are equal.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
9c8ebc14-ac0b-51cf-9234-2510839ff913
task_key
test--9c8ebc14-ac0b-51cf-9234-2510839ff913
task_revision_id
1
config / split
/ test

Official source

initial import