Some 2-adic integers related to the odd part of 2^e!
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909869944078336 |
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| author | Davis, Donald M. |
| author_facet | Davis, Donald M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some 2-adic integers related to the odd part of 2^e! Davis, Donald M. Number Theory 11A15, 11E95, 11B50 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. |
| title | Some 2-adic integers related to the odd part of 2^e! |
| topic | Number Theory 11A15, 11E95, 11B50 |
| url | https://arxiv.org/abs/2510.22078 |