{"paper":{"title":"The relationship between stopping time and number of odd terms in Collatz sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Rafael Ruggiero","submitted_at":"2019-11-01T12:33:51Z","abstract_excerpt":"The Collatz sequence for a given natural number $N$ is generated by repeatedly applying the map $N$ $\\rightarrow$ $3N+1$ if $N$ is odd and $N$ $\\rightarrow$ $N/2$ if $N$ is even. One elusive open problem in Mathematics is whether all such sequences end in 1 (Collatz conjecture), the alternative being the possibility of cycles or of unbounded sequences. In this paper, we present a formula relating the stopping time and the number of odd terms in a Collatz sequence, obtained numerically and tested for all numbers up to $10^7$ and for random numbers up to $2^{128.000}$. This result is presented a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.01229","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.01229/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}