# a recursive and dificult sequence [duplicate]

Possible Duplicate:
How to prove that this sequence converges?

Let the sequence defined recursively by the equation: $$a_n = a_{a_{n - 1} } + a_{n - a_{n - 1} }$$ How can I prove that $$\mathop {\lim }\limits_{n \to \infty } \frac{{a_n }} {n}$$

EDIT: $a_0 = a_1 = 1$ Thanks

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## marked as duplicate by t.b., Chris Eagle, Hans Lundmark, Willie WongSep 14 '11 at 14:13

If you calculate the first few terms of the sequence, you should very easily be able to conjecture a closed form for $a_n$ that works for all $n>0$. Proving the conjecture is an easy exercise in mathematical induction. And once you have that, the value of the limit is obvious.