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Actually, they searched for generalized Cullen numbers among some binary recurrence sequences. In this paper, we will work on higher order recurrence sequences. For a given linear recurrence $(G_n)_n$, under weak assumptions, and a given polynomial $T(x)\\in \\mathbb{Z}[x]$, we shall prove that if $G_n=mx^m+T(x)$, then \\[ m\\ll\\log \\log |x|\\log^2(\\log \\log |x|)\\ \\mbox{and}\\ n\\ll\\log |x|\\l"},"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":"1806.09441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-25T13:18:38Z","cross_cats_sorted":[],"title_canon_sha256":"f98e1e916818af27316d80f76a9cc62af0a00616c3283de9f024e0c95f5fcf8f","abstract_canon_sha256":"9ccd9a1566f48b40845531a14f5ea7c02db57f6caeb7fd085d7e7418562ca119"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:27.291188Z","signature_b64":"F8sfJKhjyZtHKq6Wjwug+NlmRG5E8PvX5O0KbcfS3gTPegt+20YZ87tXbrkPY+zLrHzAKLnZYgC3VeycHwCDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97dceda2cadb314c36147c7be22fbc90864177da5a4ba31b7ebf37246442456f","last_reissued_at":"2026-05-18T00:12:27.290669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:27.290669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Cullen Numbers in Linear Recurrence Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alain Togb\\' e, Diego Marques, Yuri Bilu","submitted_at":"2018-06-25T13:18:38Z","abstract_excerpt":"A Cullen number is a number of the form $m2^m+1$, where $m$ is a positive integer. 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