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In this note we consider the discriminators of a certain class of sequences, the k-regular sequences. We compute the discriminators of two such sequences, the so-called \"evil\" and \"odious\" numbers, and show they are 2-regular. We also give an example of a k-regular sequence whose discriminator is not k-regular.\n  Finally, we examine s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.00092","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-04-30T11:04:12Z","cross_cats_sorted":["cs.FL","math.NT"],"title_canon_sha256":"72ef2ea752bfb9024889a832a1782f01fb429e773f2bd723fe493f40d36850de","abstract_canon_sha256":"01723051b46016bc8c5fc8be5acc2f90b7b135b7f8af80471a08babb75975b27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:24.923634Z","signature_b64":"67Qy6xGrng3EXSGy5cocZKuOI/y7z3AO0G6q6L/WcF8Y6m7tnMk5F/CI49ALEpKQEqRERS/ilsKeptFAZxwvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e3ef67cab35aa943aec3efd62a2beae4398fcf6428b8f02e5cee10ab37f921a","last_reissued_at":"2026-05-18T01:12:24.923293Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:24.923293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discriminators and k-Regular Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.NT"],"primary_cat":"cs.DM","authors_text":"Jeffrey Shallit, Sajed Haque","submitted_at":"2016-04-30T11:04:12Z","abstract_excerpt":"The discriminator of an integer sequence s = (s(i))_{i >=0}, introduced by Arnold, Benkoski, and McCabe in 1985, is the map D_s(n) that sends n >= 1 to the least positive integer m such that the n numbers s(0), s(1), ..., s(n-1) are pairwise incongruent modulo m. In this note we consider the discriminators of a certain class of sequences, the k-regular sequences. We compute the discriminators of two such sequences, the so-called \"evil\" and \"odious\" numbers, and show they are 2-regular. 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