Answer by barak manos for Inequality on sequence of integers whose only prime...
Consider the following cases:$\small2|m_k \implies \frac32m_k\in{M} \implies m_k<m_{k+1}\leq\frac32m_k \implies \color\red{3m_k\geq2m_{k+1}}$$\small3|m_k \implies \frac43m_k\in{M} \implies...
View ArticleAnswer by Robert Israel for Inequality on sequence of integers whose only...
Hint: if $m_{k+1} = 2^p$ with $p \ge 2$, $\dfrac{3}{4} m_{k+1} \in M$.
View ArticleInequality on sequence of integers whose only prime factors are $2$ or $3$
Let $M=\lbrace 2^i 3^j | i,j \geq 0\rbrace$ and denote by $m_k$ the $k$-th element of $M$ ; so $m_1=1,m_2=2,m_3=3,m_4=4,m_5=6\ldots$.Is it true that $3m_k\geq 2m_{k+1}$ for every $k>1$ ?My thoughts...
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