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A \\textit{Cullen number} is a positive integer of the form $m\\cdot 2^m + 1$ for some integer $m \\ge 1$, while a \\textit{Woodall number} is a positive integer of the form $m\\cdot 2^m - 1$ for some integer $m \\ge 1$. In this paper, we determine all Woodall numbers in the Padovan sequence and all Cullen numbers in the Perrin sequence. Specifically, we prove t"},"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":"2605.23084","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T22:33:43Z","cross_cats_sorted":[],"title_canon_sha256":"eb67b2866ce9fac9869998ac1be25aa80c38b75c5f9681b654bba1ca19a1bd8f","abstract_canon_sha256":"afe867ec5574f6ecafa0bac69bab8356c9d0bdbebbf81ac8150409def0db843b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:37.635433Z","signature_b64":"aiUYTesh3csfVIXSNoHyR/JqrflehiH29kqMyNym+EbnxyTXB8YEdLqryQkNa5srT6tUYLEherf25rj1B+fxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d173bb8abcd6f6306d2ada72d5c3ca61fc3f9f169c74d98042e4b39ae570cae8","last_reissued_at":"2026-05-25T02:01:37.634761Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:37.634761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cullen and Woodall numbers in Padovan and Perrin sequences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eric F. Bravo, Florian Luca, Herbert Batte","submitted_at":"2026-05-21T22:33:43Z","abstract_excerpt":"Let $\\{P_n\\}_{n\\ge 0}$ and $\\{R_n\\}_{n\\ge 0}$ denote the Padovan and Perrin sequences, both satisfying the recurrence $U_{n+3} = U_{n+1} + U_n$, but with initial values $P_0 = P_1 = P_2 = 1$ and $R_0 = 3$, $R_1 = 0$, $R_2 = 2$, respectively. A \\textit{Cullen number} is a positive integer of the form $m\\cdot 2^m + 1$ for some integer $m \\ge 1$, while a \\textit{Woodall number} is a positive integer of the form $m\\cdot 2^m - 1$ for some integer $m \\ge 1$. In this paper, we determine all Woodall numbers in the Padovan sequence and all Cullen numbers in the Perrin sequence. 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