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How hard is it to look up the correct expression on Google?; edited body
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S. Carnahan ♦
S. Carnahan ♦
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This is a follow-up to the question on the Ramanujan constant.

Can one find an asymptotic family of shockingly near-integers obtained by raising e to some simple algebraic number, in the spirit of Ramanujan's $|\exp(1 + \sqrt{163}) - some integer| \le 10^{-12}$$|\exp(\pi \sqrt{163}) - \text{ some integer }| \le 10^{-12}$? Single numerical coincidences don't impress me (and for good reason too ...).

But find meIs there a sequence of such near-integers, whose nearness to integers is closer than what you know exists by pigeonholing exp(alpha) for all alpha of bounded "height" or "complexity", and then I'll really be impressed.?

This is a follow-up to the question on the Ramanujan constant.

Can one find an asymptotic family of shockingly near-integers obtained by raising e to some simple algebraic number, in the spirit of Ramanujan's $|\exp(1 + \sqrt{163}) - some integer| \le 10^{-12}$? Single numerical coincidences don't impress me (and for good reason too ...).

But find me a sequence of such near-integers, whose nearness to integers is closer than what you know exists by pigeonholing exp(alpha) for all alpha of bounded "height" or "complexity", and then I'll really be impressed.

This is a follow-up to the question on the Ramanujan constant.

Can one find an asymptotic family of shockingly near-integers obtained by raising e to some simple algebraic number, in the spirit of Ramanujan's $|\exp(\pi \sqrt{163}) - \text{ some integer }| \le 10^{-12}$? Single numerical coincidences don't impress me (and for good reason too ...).

Is there a sequence of such near-integers, whose nearness to integers is closer than what you know exists by pigeonholing exp(alpha) for all alpha of bounded "height" or "complexity"?

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fellow
fellow
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asymptotic families of ramanujan near-integers?

This is a follow-up to the question on the Ramanujan constant.

Can one find an asymptotic family of shockingly near-integers obtained by raising e to some simple algebraic number, in the spirit of Ramanujan's $|\exp(1 + \sqrt{163}) - some integer| \le 10^{-12}$? Single numerical coincidences don't impress me (and for good reason too ...).

But find me a sequence of such near-integers, whose nearness to integers is closer than what you know exists by pigeonholing exp(alpha) for all alpha of bounded "height" or "complexity", and then I'll really be impressed.