{"paper":{"title":"Integer Complexity: Experimental and Analytical Results II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J\\=anis Iraids, Juris \\v{C}er\\c{n}enoks, K\\=arlis Podnieks, M\\=arti\\c{n}\\v{s} Opmanis, Rihards Opmanis","submitted_at":"2014-09-01T15:08:34Z","abstract_excerpt":"We consider representing of natural numbers by expressions using 1's, addition, multiplication and parentheses. $\\left\\| n \\right\\|$ denotes the minimum number of 1's in the expressions representing $n$. The logarithmic complexity $\\left\\| n \\right\\|_{\\log}$ is defined as $\\left\\| n \\right\\|/{\\log_3 n}$. The values of $\\left\\| n \\right\\|_{\\log}$ are located in the segment $[3, 4.755]$, but almost nothing is known with certainty about the structure of this \"spectrum\" (are the values dense somewhere in the segment etc.). We establish a connection between this problem and another difficult proble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0446","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"}