{"id":"https://openalex.org/W7225098532","doi":"https://doi.org/10.5281/zenodo.23874359","title":"Existence of Every Term of OEIS A396673","display_name":"Existence of Every Term of OEIS A396673","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225098532","doi":"https://doi.org/10.5281/zenodo.23874359"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23874359","doi":"https://doi.org/10.5281/zenodo.23874359","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23874359","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"article-journal"},"volume":null,"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23874359","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153281072","display_name":"dr vengy","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"dr vengy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5153281072"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.93829886,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/greatest-common-divisor","display_name":"greatest common divisor","score":0.8050000071525574},{"id":"https://openalex.org/keywords/odd-primes","display_name":"odd primes","score":0.796999990940094},{"id":"https://openalex.org/keywords/chinese-remainder-theorem","display_name":"Chinese remainder theorem","score":0.7639999985694885},{"id":"https://openalex.org/keywords/admissibility","display_name":"admissibility","score":0.9390000104904175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9200999736785889},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.7269999980926514},{"id":"https://openalex.org/C188139237","wikidata":"https://www.wikidata.org/wiki/Q50706","display_name":"Square-free integer","level":2,"score":0.6344000101089478},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6055999994277954},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5275999903678894},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.5241000056266785},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.48350000381469727},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4747999906539917},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4661000072956085},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4607999920845032},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.42980000376701355},{"id":"https://openalex.org/C56781331","wikidata":"https://www.wikidata.org/wiki/Q765289","display_name":"Semiprime","level":3,"score":0.41920000314712524},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.38600000739097595},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.35409998893737793},{"id":"https://openalex.org/C102607178","wikidata":"https://www.wikidata.org/wiki/Q102761","display_name":"Least common multiple","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3441999852657318},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C64999384","wikidata":"https://www.wikidata.org/wiki/Q3507967","display_name":"Symmetrization","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23874359","doi":"https://doi.org/10.5281/zenodo.23874359","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23874359","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"article-journal"},{"id":"doi:10.5281/zenodo.23874360","doi":"https://doi.org/10.5281/zenodo.23874360","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23874360","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23874359","doi":"https://doi.org/10.5281/zenodo.23874359","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23874359","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"article-journal"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7219719644","https://openalex.org/W7222630846","https://openalex.org/W7225058505","https://openalex.org/W7225045600","https://openalex.org/W7225062249","https://openalex.org/W7225053846","https://openalex.org/W7225060167","https://openalex.org/W7220688171","https://openalex.org/W2078268996","https://openalex.org/W7214564776"],"abstract_inverted_index":{"For":[0],"every":[1,56],"odd":[2,13],"prime":[3],"\\(p\\),":[4],"we":[5],"prove":[6],"that":[7,72],"infinitely":[8],"many":[9],"triples":[10,23],"of":[11,45,84,89,106],"consecutive":[12,27],"squarefree":[14],"semiprimes":[15],"have":[16],"pairwise":[17],"greatest":[18],"common":[19],"divisor":[20],"\\(p\\).":[21,46],"These":[22],"can":[24],"be":[25],"chosen":[26],"in":[28],"the":[29,48,62,79,87],"complete":[30],"semiprime":[31],"sequence,":[32],"with":[33,66],"span":[34],"at":[35],"most":[36],"\\(pH\\),":[37],"where":[38],"\\(H>0\\)":[39],"is":[40,53,101],"an":[41],"absolute":[42],"constant":[43],"independent":[44,111],"Consequently,":[47],"first-occurrence":[49],"sequence":[50],"OEIS":[51],"A396673":[52],"well-defined":[54],"for":[55],"index":[57],"\\(n\\ge2\\).":[58],"The":[59,76,92],"proof":[60],"combines":[61],"established":[63,107],"Maynard--Tao":[64],"theorem":[65,70],"a":[67,82,104],"Chinese":[68],"remainder":[69],"construction":[71],"excludes":[73],"unwanted":[74],"semiprimes.":[75],"note":[77],"includes":[78],"congruence":[80],"construction,":[81],"verification":[83],"admissibility,":[85],"and":[86,96,100],"deduction":[88],"global":[90],"consecutiveness.":[91],"result":[93],"establishes":[94],"existence":[95],"infinite":[97],"recurrence":[98],"unconditionally":[99],"presented":[102],"as":[103],"consequence":[105],"methods,":[108],"without":[109],"asserting":[110],"novelty.":[112]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-11-03T00:00:00"}
