{"id":"https://openalex.org/W7214806004","doi":"https://doi.org/10.48550/arxiv.2609.33421","title":"A Padovan-automatic description of a nested recurrence","display_name":"A Padovan-automatic description of a nested recurrence","publication_year":2026,"publication_date":"2026-09-27","ids":{"openalex":"https://openalex.org/W7214806004","doi":"https://doi.org/10.48550/arxiv.2609.33421"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33421","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33421","pdf_url":"https://arxiv.org/pdf/2609.33421","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.33421","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5121977056","display_name":"Benoit Cloitre","orcid":"https://orcid.org/0009-0001-6778-153X","observed_orcids":["https://orcid.org/0009-0001-6778-153X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cloitre, Benoit","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140197743","display_name":"Haobo Ma","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Haobo","raw_affiliation_strings":["ChronoAI Pte Ltd ; The Omega Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ChronoAI Pte Ltd ; The Omega Institute","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5118983640","display_name":"Wenlin Zhang","orcid":"https://orcid.org/0009-0005-2414-7968","observed_orcids":["https://orcid.org/0009-0005-2414-7968"]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Zhang, Wenlin","raw_affiliation_strings":["National University of Singapore (NUS) ; The Omega Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Singapore (NUS) ; The Omega Institute","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9262999892234802,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9262999892234802,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.028200000524520874,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.01140000019222498,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discrepancy-bounds","display_name":"discrepancy bounds","score":0.5450000166893005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7324000000953674},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.5583000183105469},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49729999899864197},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49410000443458557},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4912000000476837},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.48969998955726624},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47589999437332153},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.45249998569488525},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4309999942779541},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4122999906539917},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.36629998683929443},{"id":"https://openalex.org/C25534917","wikidata":"https://www.wikidata.org/wiki/Q1326955","display_name":"Exact sequence","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C175291020","wikidata":"https://www.wikidata.org/wiki/Q1156822","display_name":"Offset (computer science)","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C2779832538","wikidata":"https://www.wikidata.org/wiki/Q2308809","display_name":"Coincidence","level":3,"score":0.2662999927997589},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33421","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33421","pdf_url":"https://arxiv.org/pdf/2609.33421","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.33421","doi":"https://doi.org/10.48550/arxiv.2609.33421","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33421","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.33421","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33421","pdf_url":"https://arxiv.org/pdf/2609.33421","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214806004.pdf","grobid_xml":"https://content.openalex.org/works/W7214806004.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1486148041","https://openalex.org/W1971464758","https://openalex.org/W2009934988","https://openalex.org/W2069336982","https://openalex.org/W2160949125","https://openalex.org/W4415084091","https://openalex.org/W6948050016"],"related_works":["https://openalex.org/W2003485139","https://openalex.org/W4249798979","https://openalex.org/W4413858721","https://openalex.org/W4390338595","https://openalex.org/W7204684831","https://openalex.org/W4411772234","https://openalex.org/W1609419359","https://openalex.org/W6903894054","https://openalex.org/W4288055827","https://openalex.org/W6904038562"],"abstract_inverted_index":{"We":[0,21,64,89,123],"study":[1],"the":[2,15,29,61,69,79,98,116,125,151],"sequence":[3],"$a(0)=0$,":[4],"$a(1)=1$":[5],"and":[6,49,76,109,140],"$a(n)=n-a(n-a(n-a(n-1)))$":[7],"for":[8,114],"$n\\ge":[9],"2$,":[10],"listed":[11],"as":[12,24],"A076502":[13],"in":[14,28,145],"On-Line":[16],"Encyclopedia":[17],"of":[18,71,82,97],"Integer":[19],"Sequences.":[20],"identify":[22],"$a(n)$":[23],"a":[25,35,56],"two-position":[26],"shift":[27],"greedy":[30],"Padovan":[31],"numeration":[32],"system,":[33],"with":[34],"finite-state":[36],"correction.":[37],"The":[38],"proof":[39],"constructs":[40],"an":[41,45,91,111,141],"addition":[42],"automaton":[43,58],"from":[44,68,84],"exact":[46,80,131,148],"integer-carry":[47],"invariant":[48],"certifies":[50],"its":[51,103],"completeness":[52],"by":[53],"finite-language":[54],"inclusion;":[55],"synchronized":[57],"then":[59],"verifies":[60],"nested":[62],"recurrence.":[63],"establish":[65],"bounded":[66],"discrepancy":[67,118,129],"line":[70],"slope":[72],"$c$,":[73],"where":[74],"$c^3-c^2+2c-1=0$,":[75],"show":[77],"that":[78,102],"set":[81],"offsets":[83],"$\\lfloor":[85],"cn\\rfloor$":[86],"is":[87,107],"$\\{-1,0,1,2\\}$.":[88],"construct":[90],"explicit":[92],"26-letter":[93],"non-erasing":[94],"morphic":[95,135],"presentation":[96],"first-difference":[99],"word,":[100],"prove":[101],"least":[104,137],"balance":[105,138],"constant":[106],"4,":[108],"give":[110],"effective":[112,142],"procedure":[113],"enclosing":[115],"global":[117],"extrema":[119,143],"to":[120],"arbitrary":[121],"accuracy.":[122],"formalize":[124],"recurrence":[126],"identification,":[127],"six-decimal":[128],"bound,":[130],"offset":[132],"set,":[133],"concrete":[134],"identity,":[136],"constant,":[139],"algorithm":[144],"Lean.":[146],"Separate":[147],"computations":[149],"refine":[150],"numerical":[152],"enclosures.":[153]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}