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Chris Wuthrich
Chris Wuthrich
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Given a prime number $p$ and an integer $0<a_0<p$. Consider a sequence $a_i=p \mod a_{i-1}$, where $p$ is a prime number, how. How to estimate the smallest $i$ where $a_i=1$? $a_0$ is a positive integer and is guaranteed to be less than $p$.
I

I tried some prime numbers, and found that such $i$ is always small. I have never found an $i$ larger than 50 when $p$ is smaller than $10^7$. How to estimate the upper bound of $i$?

Consider a sequence $a_i=p \mod a_{i-1}$, where $p$ is a prime number, how to estimate the smallest $i$ where $a_i=1$? $a_0$ is a positive integer and is guaranteed to be less than $p$.
I tried some prime numbers, and found that such $i$ is always small. I have never found an $i$ larger than 50 when $p$ is smaller than $10^7$. How to estimate the upper bound of $i$?

Given a prime number $p$ and an integer $0<a_0<p$. Consider a sequence $a_i=p \mod a_{i-1}$. How to estimate the smallest $i$ where $a_i=1$?

I tried some prime numbers, and found that such $i$ is always small. I have never found an $i$ larger than 50 when $p$ is smaller than $10^7$. How to estimate the upper bound of $i$?

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zbh2047
zbh2047
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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 $a_i=1$?

Consider a sequence $a_i=p \mod a_{i-1}$, where $p$ is a prime number, how to estimate the smallest $i$ where $a_i=1$? $a_0$ is a positive integer and is guaranteed to be less than $p$.
I tried some prime numbers, and found that such $i$ is always small. I have never found an $i$ larger than 50 when $p$ is smaller than $10^7$. How to estimate the upper bound of $i$?