{"paper":{"title":"Continued fraction normality is not preserved along arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Byron Heersink, Joseph Vandehey","submitted_at":"2015-09-18T04:00:46Z","abstract_excerpt":"It is well known that if $0.a_1a_2a_3\\dots$ is the base-$b$ expansion of a number normal to base-$b$, then the numbers $0.a_ka_{m+k}a_{2m+k}\\dots$ for $m\\ge 2$, $k\\ge 1$ are all normal to base-$b$ as well.\n  In contrast, given a continued fraction expansion $\\langle a_1,a_2,a_3,\\dots\\rangle$ that is normal (now with respect to the continued fraction expansion), we show that for any integers $m\\ge 2$, $k\\ge 1$, the continued fraction $\\langle a_k, a_{m+k},a_{2m+k},a_{3m+k},\\dots\\rangle$ will never be normal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05501","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"}