Continued Fraction Expansion of e
[2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, 1, 1, 16, 1, 1, 18...] Holy smokes! The even integers just continue pumping out every three partial quotients, to infinity and beyond!
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