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More generally, what is the largest integer $g_s$ that has exactly $s$ such representations? We illustrate a family of parameters, based on a recent paper by Tripathi, whose generalized Frobenius numbers $g_0, \\ g_1, \\ g_2, ...$ exhibit unnatural jumps; namely, $g_0, \\ g_1, \\ g_k, \\ g_{\\binom{k+1}{k-1}}, \\ g_{\\binom{k+2}{k-1}}, ...$ form an arithmetic progression, a"},"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":"1005.2692","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-15T18:19:51Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"77645aaed9283a57a11c98a77331b275e2b75a39e2dda3973b880eddfae221fd","abstract_canon_sha256":"5994c4bff01206709f4904bf33d8a792bb0234570bafd3c4893ed25df333718e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:24.334346Z","signature_b64":"09R4pskkrTgSwni6wOnyskmPfiazu7ckDAZe0ikQNMnZX0ljQJksX1YP3aiXCb5xPUKBUjIzu9MfWjz7xfSBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9c388a64c32be20be09b037659e18449311def25275c7a01431cb6b6b9991c2","last_reissued_at":"2026-05-18T03:11:24.333525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:24.333525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Extreme Family of Generalized Frobenius Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Curtis Kifer, Matthias Beck","submitted_at":"2010-05-15T18:19:51Z","abstract_excerpt":"We study a generalization of the \\emph{Frobenius problem}: given $k$ positive relatively prime integers, what is the largest integer $g_0$ that cannot be represented as a nonnegative integral linear combination of these parameters? 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