Using Walnut to solve problems from the OEIS
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915184084254720 |
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| author | Bosma, Wieb Bruin, Rene Fokkink, Robbert Grube, Jonathan Reuijl, Anniek Tromp, Thian |
| author_facet | Bosma, Wieb Bruin, Rene Fokkink, Robbert Grube, Jonathan Reuijl, Anniek Tromp, Thian |
| contents | We use the automatic theorem prover Walnut to resolve various open problems from the OEIS and beyond. Specifically, we clarify the structure of sequence A260311, which concerns runs of sums of upper Wythoff numbers. We extend a result of Hajdu, Tijdeman, and Varga on polynomials with nonzero coefficients modulo a prime. Additionally, we settle open problems related to the anti-recurrence sequences A265389 and A299409, as well as the subsumfree sequences A026471 and A026475. Our findings also give rise to new open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Using Walnut to solve problems from the OEIS Bosma, Wieb Bruin, Rene Fokkink, Robbert Grube, Jonathan Reuijl, Anniek Tromp, Thian Number Theory Combinatorics 11B37, 11R09, 68R15 We use the automatic theorem prover Walnut to resolve various open problems from the OEIS and beyond. Specifically, we clarify the structure of sequence A260311, which concerns runs of sums of upper Wythoff numbers. We extend a result of Hajdu, Tijdeman, and Varga on polynomials with nonzero coefficients modulo a prime. Additionally, we settle open problems related to the anti-recurrence sequences A265389 and A299409, as well as the subsumfree sequences A026471 and A026475. Our findings also give rise to new open problems. |
| title | Using Walnut to solve problems from the OEIS |
| topic | Number Theory Combinatorics 11B37, 11R09, 68R15 |
| url | https://arxiv.org/abs/2503.04122 |