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Omni-MATH / A sequence of positive integers a₁,a₂,a₃,… satisfies a_(n+1)=n⌊(a_(n))/(n)⌋+1 for all positive integers n. If a₃₀=30, how many possible values can a₁ take? (For a real number x, …

Problem

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problem

A sequence of positive integers a1,a2,a3,…a_{1}, a_{2}, a_{3}, \ldots satisfies an+1=n⌊ann⌋+1a_{n+1}=n\left\lfloor\frac{a_{n}}{n}\right\rfloor+1 for all positive integers nn. If a30=30a_{30}=30, how many possible values can a1a_{1} take? (For a real number xx, ⌊x⌋\lfloor x\rfloor denotes the largest integer that is not greater than xx.)
Plain-text mathematical notation (without MathML)
A sequence of positive integers a₁,a₂,a₃,… satisfies a_(n+1)=n⌊(a_(n))/(n)⌋+1 for all positive integers n. If a₃₀=30, how many possible values can a₁ take? (For a real number x, ⌊x⌋ denotes the largest integer that is not greater than x.)
Original LaTeX notation
A sequence of positive integers $a_{1}, a_{2}, a_{3}, \ldots$ satisfies $$a_{n+1}=n\left\lfloor\frac{a_{n}}{n}\right\rfloor+1$$ for all positive integers $n$. If $a_{30}=30$, how many possible values can $a_{1}$ take? (For a real number $x$, $\lfloor x\rfloor$ denotes the largest integer that is not greater than $x$.)

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Source and history

task_id
57cc79d7-ad93-54ec-b3bf-0ba395cc28a8
task_key
test--57cc79d7-ad93-54ec-b3bf-0ba395cc28a8
task_revision_id
1
config / split
/ test

Official source

initial import