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Your question is a special case of the question that I answered in complete detail here, where I gave an explicit fast algorithm that can be used to compute the return times to any interval. Your problem is essentially the case of $\alpha =0$, which is especially easy to compute. The integers you are asking for are very evenly spaced- a generalized arithmetic progression with two alternating moduli. So yes, the distance between consecutive integers that do what you want is bounded.

Your question is a special case of the question that I answered in complete detail here, where I gave an explicit fast algorithm that can be used to compute the return times to any interval. Your problem is essentially the case of $\alpha =0$, which is especially easy to compute. The integers you are asking for are very evenly spaced- a generalized arithmetic progression with two alternating moduli. So yes, the distance between consecutive integers that do what you want is bounded.

If you want an easily computable answer, as Asaf says you should use continued fractions. Your question is a special case of the question that I answered here, where I gave an explicit algorithm to compute the return times to any interval. It is the case of $\alpha =0$, which is especially easy and fast to compute. The integers you are asking for are very evenly spaced- like an arithmetic progression with two moduli. So yes, the distance between consecutive integers that do what you want is bounded.

Your question is a special case of the question that I answered in complete detail here, where I gave an explicit fast algorithm that can be used to compute the return times to any interval. Your problem is essentially the case of $\alpha =0$, which is especially easy to compute. The integers you are asking for are very evenly spaced- a generalized arithmetic progression with two alternating moduli. So yes, the distance between consecutive integers that do what you want is bounded.

If you want an easily computable answer, as Asaf says you should use continued fractions. Your question is a special case of the question that I answered here, where I gave an explicit algorithm to compute the return times to any interval. They are very evenly spaced- like an arithmetic progression with two moduli. So yes, the distance between consecutive integers that do what you want is bounded.

If you want an easily computable answer, as Asaf says you should use continued fractions. Your question is a special case of the question that I answered here, where I gave an explicit algorithm to compute the return times to any interval. It is the case of $\alpha =0$, which is especially easy and fast to compute. The integers you are asking for are very evenly spaced- like an arithmetic progression with two moduli. So yes, the distance between consecutive integers that do what you want is bounded.