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I am trying to figure out if a sequence $a_{n+1} = a_n - \frac{1}{a_n}$ is bounded, but I don't see how to approach the question. The behavior of the first million members seem erratic and the standard methods don't seem to apply.

What is the right way to find out if the sequence is bounded?

a0 = 0
a1 = 2

for i in range(108):
    if i%105 == 0:
        print(a1)
    a0 = a1
    a1 = a0-(1/a0)

Update

math.stackexchange.com/q/2226876/42969 doesnot answer the question definitively. tends to support the hypothesis is not the same as proven to be. Is there any progress on this topic?

sixtytrees
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    Your code and your post say different things. In your code, it seems like you defined $a_{n+1} = a_n - 1/a_n$ and in the post you have $a_{n+1} = a_n - \frac{1}{1/a_n}.$ Edit it to make clear exactly what you want. – xyz Dec 12 '23 at 09:54
  • https://math.stackexchange.com/q/2226876/42969, https://math.stackexchange.com/q/1690150/42969 – Martin R Dec 12 '23 at 09:58
  • People are redirecting to posts that don't actually prove or disprove that the sequence is bounded... – PierreCarre Dec 12 '23 at 12:07

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