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zbh2047
  • Member for 6 years, 10 months
  • Last seen more than 2 years ago
  • Beijing, China
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Consider a sequence $a_i=p \mod a_{i-1}$, where $p$ is a prime number, how to estimate the smallest $i$ where $a_i=1$?
Is there a tight bound of $p$? $\sqrt p$ is about 3000 when $p=10^7$, but results shows that it is never larger than 50.
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Consider a sequence $a_i=p \mod a_{i-1}$, where $p$ is a prime number, how to estimate the smallest $i$ where $a_i=1$?
I want a bound which only depends on $p$. That is, for any $0<a_0<p$, the bound is always correct. Your understanding and modification is really helpful. Thanks!
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Consider a sequence $a_i=p \mod a_{i-1}$, where $p$ is a prime number, how to estimate the smallest $i$ where $a_i=1$?
I mean the only $i$ such that $a_i=1$. In fact, I just wonder why such $i$ are always small, for any $p$ and $a_0$. I guess such $i$ is equal to $O(\log p)$, for example.
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