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I have some problems, with the convergence of this sequence defined recursively. It's clear that it's bounded. But is it convergent? How can I check for convergence?

$$ a_0 = a_1 = 1 $$

$$ a_n = a_{a_{n - 1} } + a_{n - a_{n - 1} } $$

How do I prove that the sequence $\frac{a_n}{n}$ converges? I tried but am not able to do it.

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    I think the sequence is Hofstadter-Conway $10000 Sequence! http://mathworld.wolfram.com/Hofstadter-Conway10000-DollarSequence.html2011-08-17
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    but i can´t prove that it converges <.<, i don´t care the value, only that converges )=2011-08-17
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    "$a_0=a_1=a_n$"?2011-08-17
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    @Daniel: I edited the initial conditions, please check to see if that is what you intended. The original statement doesn't make sense.2011-08-17
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    @Jineon: the initial conditions, however, are key. If you specify $a_0 = a_1 = 1$, then inductively if $a_n = n$, then $a_{n+1} = a_n + a_{n+1 - n} = n + 1$, showing that $\lim a_k/k = 1$.2011-08-17

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