Some 2-adic integers related to the odd part of 2e!
Abstract
The odd part of 2e! as e approaches infinity leads to a 2-adic integer z. The bits of z were publicized in OEIS-A359349, where two conjectures were made, relevant to computing z. We prove both of those conjectures. A second 2-adic integer, the limit of ((2e-1)!!-1)/2e, plays a key role in one proof.
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