{"paper":{"title":"The minimal growth of a $k$-regular sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jason P. Bell, Kevin G. Hare, Michael Coons","submitted_at":"2014-10-21T01:59:48Z","abstract_excerpt":"We determine a lower gap property for the growth of an unbounded \\(\\mathbb{Z}\\)-valued \\(k\\)-regular sequence. In particular, if \\(f:\\mathbb{N}\\to\\mathbb{Z}\\) is an unbounded \\(k\\)-regular sequence, we show that there is a constant \\(c>0\\) such that \\(|f(n)|>c\\log n\\) infinitely often. We end our paper by answering a question of Borwein, Choi, and Coons on the sums of completely multiplicative automatic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5517","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}