{"paper":{"title":"Infinite Sidon sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Javier Cilleruelo","submitted_at":"2012-09-03T12:23:27Z","abstract_excerpt":"We present a new method to obtain infinite Sidon sequences, based on the discrete logarithm. We construct an infinite Sidon sequence A, with A(x)= x^{\\sqrt 2-1+o(1)}. Ruzsa proved the existence of a Sidon sequence with similar counting function but his proof was not constructive.\n  Our method generalizes to B_h sequences: For all h\\ge 3, there is a B_h sequence A such that A(x)=x^{\\sqrt{(h-1)^2+1}-(h-1)+o(1)}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0326","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":""},"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"}