{"paper":{"title":"Counting non-standard binary representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Katie Anders","submitted_at":"2015-09-03T21:46:25Z","abstract_excerpt":"Let $\\mathcal{A}$ be a finite subset of $\\mathbb{N}$ including $0$ and $f_\\mathcal{A}(n)$ be the number of ways to write $n=\\sum_{i=0}^{\\infty}\\epsilon_i2^i$, where $\\epsilon_i\\in\\mathcal{A}$. We consider asymptotics of the summatory function $s_\\mathcal{A}(r,m)$ of $f_\\mathcal{A}(n)$ from $m2^r$ to $m2^{r+1}-1$ and show that $s_{\\mathcal{A}}(r,m)\\approx c(\\mathcal{A},m)\\left|\\mathcal{A}\\right|^r$ for some $c(\\mathcal{A},m)\\in\\mathbb{Q}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01285","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"}