{"id":"https://openalex.org/W2036403999","doi":"https://doi.org/10.1090/s0025-5718-99-01031-5","title":"Maximum excursion and stopping time record-holders for the problem: Computational results","display_name":"Maximum excursion and stopping time record-holders for the problem: Computational results","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2036403999","doi":"https://doi.org/10.1090/s0025-5718-99-01031-5","mag":"2036403999"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-99-01031-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01031-5","pdf_url":"https://www.ams.org/mcom/1999-68-225/S0025-5718-99-01031-5/S0025-5718-99-01031-5.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/1999-68-225/S0025-5718-99-01031-5/S0025-5718-99-01031-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047325808","display_name":"Tom\u00e1s Oliveira e Silva","orcid":"https://orcid.org/0000-0002-8878-3219"},"institutions":[{"id":"https://openalex.org/I4210125590","display_name":"Institute for Systems Engineering and Computers","ror":"https://ror.org/033wn8m60","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210125590"]},{"id":"https://openalex.org/I60858718","display_name":"University of Aveiro","ror":"https://ror.org/00nt41z93","country_code":"PT","type":"education","lineage":["https://openalex.org/I60858718"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Tom\u00e1s e Silva","raw_affiliation_strings":["Departamento de Electr\u00c3\u00b3nica e Telecomunica\u00c3\u00a7\u00c3\u00b5es / INESC Aveiro, Universidade de Aveiro, 3810 Aveiro, Portugal","Departamento de Electr\u00f3nica e Telecomunica\u00e7\u00f5es / INESC Aveiro, Universidade de Aveiro, 3810 Aveiro, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Electr\u00c3\u00b3nica e Telecomunica\u00c3\u00a7\u00c3\u00b5es / INESC Aveiro, Universidade de Aveiro, 3810 Aveiro, Portugal","institution_ids":["https://openalex.org/I4210125590","https://openalex.org/I60858718"]},{"raw_affiliation_string":"Departamento de Electr\u00f3nica e Telecomunica\u00e7\u00f5es / INESC Aveiro, Universidade de Aveiro, 3810 Aveiro, Portugal","institution_ids":["https://openalex.org/I60858718"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047325808"],"corresponding_institution_ids":["https://openalex.org/I4210125590","https://openalex.org/I60858718"],"apc_list":null,"apc_paid":null,"fwci":1.938,"has_fulltext":true,"cited_by_count":49,"citation_normalized_percentile":{"value":0.86463852,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"68","issue":"225","first_page":"371","last_page":"384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10127","display_name":"Banking stability, regulation, efficiency","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9764000177383423,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7277481555938721},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4232650399208069},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37559372186660767},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3711361885070801}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7277481555938721},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4232650399208069},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37559372186660767},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3711361885070801}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-99-01031-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01031-5","pdf_url":"https://www.ams.org/mcom/1999-68-225/S0025-5718-99-01031-5/S0025-5718-99-01031-5.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/s0025-5718-99-01031-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01031-5","pdf_url":"https://www.ams.org/mcom/1999-68-225/S0025-5718-99-01031-5/S0025-5718-99-01031-5.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/W2036403999.pdf","grobid_xml":"https://content.openalex.org/works/W2036403999.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1991036063","https://openalex.org/W2012709580","https://openalex.org/W2014656163","https://openalex.org/W2076882011","https://openalex.org/W4246319563"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2386767533"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"some":[3],"results":[4,73],"concerning":[5],"the":[6,12,94,98,253],"search":[7],"for":[8,52,76],"initial":[9,55,69,78],"values":[10],"to":[11,39,193,278],"so-called":[13],"<inline-formula":[14,81,106,137,169,194,254],"content-type=\"math/mathml\">":[15,82,107,138,170,195,255],"<mml:math":[16,83,108,139,171,196,256],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[17,84,109,140,172,197,257],"alttext=\"3":[18,258],"x":[19,259],"plus":[20,260],"1\">":[21,261],"<mml:semantics>":[22,86,116,145,174,212,262],"<mml:mrow>":[23,117,146,213,263],"<mml:mn>3</mml:mn>":[24,216,264],"<mml:mi>x</mml:mi>":[25,265],"<mml:mo>+</mml:mo>":[26,266],"<mml:mn>1</mml:mn>":[27,267],"</mml:mrow>":[28,128,153,225,239,241,268],"<mml:annotation":[29,88,129,154,176,242,269],"encoding=\"application/x-tex\">3x+1</mml:annotation>":[30,270],"</mml:semantics>":[31,90,132,156,178,249,271],"</mml:math>":[32,91,133,157,179,250,272],"</inline-formula>":[33,92,134,158,180,251,273],"problem":[34],"which":[35,58,189],"give":[36],"rise":[37],"either":[38,159],"function":[40,50,99,167],"iterates":[41,51,100],"that":[42,75,279],"attain":[43],"a":[44,60,160,163,183],"maximum":[45,95],"value":[46,79,96],"higher":[47,63],"than":[48,64],"all":[49,53,67],"smaller":[54,68],"values,":[56],"or":[57,162],"have":[59],"stopping":[61],"time":[62],"those":[65],"of":[66,80,97,168,185],"values.":[70],"Our":[71],"computational":[72],"suggest":[74],"an":[77],"alttext=\"n\">":[85,173],"<mml:mi>n</mml:mi>":[87,119,125,150,175,214],"encoding=\"application/x-tex\">n</mml:annotation>":[89,177],",":[93,135,252],"is":[101],"bounded":[102],"from":[103],"above":[104],"by":[105],"alttext=\"n":[110,198],"squared":[111],"f":[112],"left-parenthesis":[113,142],"n":[114,143],"right-parenthesis\">":[115,144],"<mml:msup>":[118,220,234],"<mml:mn>2</mml:mn>":[120,221],"</mml:msup>":[121,226,240],"<mml:mi>f</mml:mi>":[122,147],"<mml:mo":[123,126,148,151],"stretchy=\"false\">(</mml:mo>":[124,149],"stretchy=\"false\">)</mml:mo>":[127,152],"encoding=\"application/x-tex\">n^2":[130],"f(n)</mml:annotation>":[131],"with":[136],"alttext=\"f":[141],"encoding=\"application/x-tex\">f(n)</mml:annotation>":[155],"constant":[161],"very":[164],"slowly":[165],"increasing":[166],".":[181],"As":[182],"by-product":[184],"this":[186],"(exhaustive)":[187],"search,":[188],"was":[190,275],"performed":[191],"up":[192,277],"equals":[199],"3":[200],"dot":[201,208],"2":[202],"Superscript":[203,210],"53":[204],"Baseline":[205],"almost-equals":[206],"2.702":[207,246],"10":[209],"16\">":[211],"<mml:mo>=</mml:mo>":[215],"<mml:mo>":[217,227,231],"\u22c5":[218,232],"</mml:mo>":[219,229,233],"<mml:mrow":[222,236],"class=\"MJX-TeXAtom-ORD\">":[223,237],"<mml:mn>53</mml:mn>":[224],"\u2248":[228],"<mml:mn>2.702</mml:mn>":[230],"<mml:mn>10</mml:mn>":[235],"<mml:mn>16</mml:mn>":[238],"encoding=\"application/x-tex\">n=3":[243],"\\cdot":[244,247],"2^{53}\\approx":[245],"10^{16}</mml:annotation>":[248],"conjecture":[274],"verified":[276],"same":[280],"number.":[281]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}