{"id":"https://openalex.org/W1970594294","doi":"https://doi.org/10.1090/s0025-5718-96-00707-7","title":"\ud835\udc51-complete sequences of integers","display_name":"\ud835\udc51-complete sequences of integers","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W1970594294","doi":"https://doi.org/10.1090/s0025-5718-96-00707-7","mag":"1970594294"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-96-00707-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00707-7","pdf_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00707-7/S0025-5718-96-00707-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00707-7/S0025-5718-96-00707-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037065021","display_name":"P\u00e9ter L. Erd\u0151s","orcid":"https://orcid.org/0000-0002-1139-2316"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]}],"countries":["HU","IL"],"is_corresponding":false,"raw_author_name":"P. Erdos","raw_affiliation_strings":["Mathematical Institute, Hungarian Academy of Sciences, Realtanoda u. 13-15, H-1053 Budapest, Hungary and Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Hungarian Academy of Sciences, Realtanoda u. 13-15, H-1053 Budapest, Hungary and Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I174306211","https://openalex.org/I7597260"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111689319","display_name":"Mordechai Lewin","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Mordechai Lewin","raw_affiliation_strings":["Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel","Department Of Mathematics , Technion-Israel Institute Of Technology , Haifa, 32000, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Department Of Mathematics , Technion-Israel Institute Of Technology , Haifa, 32000, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9264,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.83943275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"65","issue":"214","first_page":"837","last_page":"840"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9438999891281128,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6707034707069397},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.5539735555648804},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4941599667072296},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4414587616920471}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6707034707069397},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.5539735555648804},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4941599667072296},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4414587616920471}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-96-00707-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00707-7","pdf_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00707-7/S0025-5718-96-00707-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-96-00707-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00707-7","pdf_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00707-7/S0025-5718-96-00707-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1970594294.pdf","grobid_xml":"https://content.openalex.org/works/W1970594294.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2116777488","https://openalex.org/W4232801683"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W2625833328","https://openalex.org/W1533177136","https://openalex.org/W4380994516"],"abstract_inverted_index":{"An":[0],"infinite":[1],"sequence":[2],"<inline-formula":[3,36,59,85,103,146,200],"content-type=\"math/mathml\">":[4,37,60,86,104,147,201],"<mml:math":[5,38,61,87,105,148,202],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[6,39,62,88,106,149,203],"alttext=\"a":[7,63],"1":[8],"greater-than":[9,12],"a":[10],"2":[11],"midline-horizontal-ellipsis\">":[13],"<mml:semantics>":[14,41,66,90,117,164,209],"<mml:mrow>":[15,118,165,210],"<mml:msub>":[16,21,67],"<mml:mi>a</mml:mi>":[17,22,68],"<mml:mn>1</mml:mn>":[18],"</mml:msub>":[19,24,70],"<mml:mo>&gt;</mml:mo>":[20,25],"<mml:mn>2</mml:mn>":[23],"<mml:mo>":[26],"\u22ef":[27],"</mml:mo>":[28],"</mml:mrow>":[29,137,190,222],"<mml:annotation":[30,43,71,92,138,191,223],"encoding=\"application/x-tex\">a_1&gt;a_2&gt;\\dotsb</mml:annotation>":[31],"</mml:semantics>":[32,45,73,94,142,196,227],"</mml:math>":[33,46,74,95,143,197,228],"</inline-formula>":[34,47,75,96,144,198,229],"is":[35,55],"alttext=\"d\">":[40,89],"<mml:mi>d</mml:mi>":[42,91],"encoding=\"application/x-tex\">d</mml:annotation>":[44,93],"-":[48],"<italic>complete</italic>":[49],"if":[50],"every":[51],"sufficiently":[52],"large":[53],"integer":[54],"the":[56,81,101],"sum":[57],"of":[58,98,100],"Subscript":[64],"i\">":[65],"<mml:mi>i</mml:mi>":[69],"encoding=\"application/x-tex\">a_i</mml:annotation>":[72],"such":[76],"that":[77],"no":[78],"one":[79],"divides":[80],"other.":[82],"We":[83],"investigate":[84],"-completeness":[97],"sets":[99],"form":[102],"alttext=\"left-brace":[107,150],"p":[108,151],"Superscript":[109,113,152,156,160],"alpha":[110,153],"Baseline":[111,115,154,158,162],"q":[112,155],"beta":[114,157,206],"right-brace\">":[116,163],"<mml:mo":[119,134,166,187],"fence=\"false\"":[120,135,167,188],"stretchy=\"false\">{</mml:mo>":[121,168],"<mml:msup>":[122,128,169,175,181],"<mml:mi>p</mml:mi>":[123,170],"<mml:mi>":[124,130,171,177,183,211,215,219],"\u03b1":[125,172,212],"</mml:mi>":[126,132,173,179,185,213,217,221],"</mml:msup>":[127,133,174,180,186],"<mml:mi>q</mml:mi>":[129,176],"\u03b2":[131,178,216],"stretchy=\"false\">}</mml:mo>":[136,189],"encoding=\"application/x-tex\">\\{p^\\alpha":[139,192],"q^\\beta":[140,193],"\\}</mml:annotation>":[141,195],"and":[145],"r":[159],"gamma":[161],"<mml:mi>r</mml:mi>":[182],"\u03b3":[184,220],"r^\\gamma":[194],"with":[199],"alttext=\"alpha":[204],"comma":[205,207],"gamma\">":[208],"<mml:mo>,</mml:mo>":[214,218],"encoding=\"application/x-tex\">\\alpha":[224],",\\beta":[225],",\\gamma</mml:annotation>":[226],"nonnegative.":[230]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
