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Omni-MATH / Mary has a sequence m₂,m₃,m₄,…, such that for each b≥2,m_(b) is the least positive integer m for which none of the base-b logarithms log_(b)(m),log_(b)(m+1),…,log_(b)(m+2017) are i…

Problem

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problem

Mary has a sequence m2,m3,m4,…m_{2}, m_{3}, m_{4}, \ldots, such that for each b≥2,mbb \geq 2, m_{b} is the least positive integer mm for which none of the base-bb logarithms logb(m),logb(m+1),…,logb(m+2017)\log _{b}(m), \log _{b}(m+1), \ldots, \log _{b}(m+2017) are integers. Find the largest number in her sequence.
Plain-text mathematical notation (without MathML)
Mary has a sequence m₂,m₃,m₄,…, such that for each b≥2,m_(b) is the least positive integer m for which none of the base-b logarithms log_(b)(m),log_(b)(m+1),…,log_(b)(m+2017) are integers. Find the largest number in her sequence.
Original LaTeX notation
Mary has a sequence $m_{2}, m_{3}, m_{4}, \ldots$, such that for each $b \geq 2, m_{b}$ is the least positive integer $m$ for which none of the base-$b$ logarithms $\log _{b}(m), \log _{b}(m+1), \ldots, \log _{b}(m+2017)$ are integers. Find the largest number in her sequence.

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Source and history

task_id
0afc51ef-47c1-51c4-b3af-a578900ce11b
task_key
test--0afc51ef-47c1-51c4-b3af-a578900ce11b
task_revision_id
1
config / split
/ test

Official source

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