{"paper":{"title":"Numerical Analogues of Aronson's Sequence","license":"","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.NT","authors_text":"Benoit Cloitre, Matthew J. Vandermast, N. J. A. Sloane","submitted_at":"2003-05-21T21:56:26Z","abstract_excerpt":"Aronson's sequence 1, 4, 11, 16, ... is defined by the English sentence ``t is the first, fourth, eleventh, sixteenth, ... letter of this sentence.'' This paper introduces some numerical analogues, such as: a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition ``n is a member of the sequence if and only if a(n) is odd.'' This sequence can also be characterized by its ``square'', the sequence a^(2)(n) = a(a(n)), which equals 2n+3 for n >= 1. There are many generalizations of this sequence, some of which are new, while others throw new light"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305308","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"}