Some 2-adic integers related to the odd part of 2^e!
Number Theory
2025-10-28 v1
Abstract
The odd part of 2^e! 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 ((2^e-1)!!-1)/2^e, plays a key role in one proof.
Keywords
Cite
@article{arxiv.2510.22078,
title = {Some 2-adic integers related to the odd part of 2^e!},
author = {Donald M. Davis},
journal= {arXiv preprint arXiv:2510.22078},
year = {2025}
}