{"paper":{"title":"Disquisitiones Arithmeticae and online sequence A108345","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Monsky","submitted_at":"2010-09-21T02:48:31Z","abstract_excerpt":"Let g be the element that is the sum of x^(n^2) for n >= 0 of A=Z/2[[x]], and let B consist of all n for which the coefficient of x^n in 1/g is 1. (The elements of B are the entries 0, 1, 2, 3, 5, 7, 8, 9, 13, ... in A108345; see The On-Line Encyclopedia of Integer Sequences (OEIS).) Cooper, Eichhorn, and O'Bryant [1] have shown that the (upper) density of B is at most 1/4, and it is conjectured that B has density 0. This note uses results of Gauss on sums of 3 squares to show that the subset of B consisting of all n not congruent to 15 mod 16 has density 0. The final section gives some comput"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3985","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"}