{"paper":{"title":"Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Doron Zeilberger, N. J. A. Sloane, Shalosh B. Ekhad","submitted_at":"2016-09-19T00:06:27Z","abstract_excerpt":"Pisot sequences (sequences $a_n$ with initial terms $a_0=x, a_1=y$, and defined for $n>1$ by $a_n= \\lfloor a_{n-1}^2/a_{n-2} + \\frac{1}{2} \\rfloor$) often satisfy linear recurrences with constant coefficients that are valid for all $n \\geq 0$, but there are also cautionary examples where there is a linear recurrence that is valid for an initial range of values of $n$ but fails to be satisfied beyond that point, providing further illustrations of Richard Guy's celebrated \"Strong Law of Small Numbers\". In this paper we present a decision algorithm, fully implemented in an accompanying Maple prog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05570","kind":"arxiv","version":3},"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"}