{"paper":{"title":"An Unusual Continued Fraction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dzmitry Badziahin, Jeffrey Shallit","submitted_at":"2015-05-04T14:57:46Z","abstract_excerpt":"We consider the real number $\\sigma$ with continued fraction expansion $[a_0, a_1, a_2,\\ldots] = [1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,16,\\ldots]$, where $a_i$ is the largest power of $2$ dividing $i+1$. We compute the irrationality measure of $\\sigma^2$ and demonstrate that $\\sigma^2$ (and $\\sigma$) are both transcendental numbers. We also show that certain partial quotients of $\\sigma^2$ grow doubly exponentially, thus confirming a conjecture of Hanna and Wilson."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00667","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"}