{"id":"https://openalex.org/W1680596605","doi":"https://doi.org/10.1080/10586458.2016.1204638","title":"A Hidden Signal in the Ulam Sequence","display_name":"A Hidden Signal in the Ulam Sequence","publication_year":2016,"publication_date":"2016-09-13","ids":{"openalex":"https://openalex.org/W1680596605","doi":"https://doi.org/10.1080/10586458.2016.1204638","mag":"1680596605"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2016.1204638","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2016.1204638","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1507.00267","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054778975","display_name":"Stefan Steinerberger","orcid":"https://orcid.org/0000-0002-7745-4217"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stefan Steinerberger","raw_affiliation_strings":["Department of Mathematics, Yale University, New Haven, CT, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yale University, New Haven, CT, USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054778975"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":null,"apc_paid":null,"fwci":0.5549,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62061132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"26","issue":"4","first_page":"460","last_page":"467"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9883999824523926,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9879999756813049,"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/sequence","display_name":"Sequence (biology)","score":0.735148549079895},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6552614569664001},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6177455186843872},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5553622245788574},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.49737265706062317},{"id":"https://openalex.org/keywords/phenomenon","display_name":"Phenomenon","score":0.47040921449661255},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4567060172557831},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3774232566356659},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3227512836456299},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19288358092308044},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.130808025598526},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1273769736289978}],"concepts":[{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.735148549079895},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6552614569664001},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6177455186843872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5553622245788574},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.49737265706062317},{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.47040921449661255},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4567060172557831},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3774232566356659},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3227512836456299},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19288358092308044},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.130808025598526},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1273769736289978},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10586458.2016.1204638","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2016.1204638","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1507.00267","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.00267","pdf_url":"https://arxiv.org/pdf/1507.00267","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},{"id":"mag:1680596605","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1507.00267.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1507.00267","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1507.00267","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1507.00267","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.00267","pdf_url":"https://arxiv.org/pdf/1507.00267","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1680596605.pdf","grobid_xml":"https://content.openalex.org/works/W1680596605.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W348908286","https://openalex.org/W1520128606","https://openalex.org/W1624294673","https://openalex.org/W1971731573","https://openalex.org/W1975234853","https://openalex.org/W2012928041","https://openalex.org/W2026175932","https://openalex.org/W2028435095","https://openalex.org/W2052840430","https://openalex.org/W2077055049","https://openalex.org/W2108900323","https://openalex.org/W2115034958","https://openalex.org/W2126209209","https://openalex.org/W2144143005","https://openalex.org/W2493628447","https://openalex.org/W2588588830","https://openalex.org/W3013996454","https://openalex.org/W4241126601","https://openalex.org/W4402911783"],"related_works":["https://openalex.org/W1078482883","https://openalex.org/W2798878397","https://openalex.org/W2964044319","https://openalex.org/W2054409620","https://openalex.org/W3204665133","https://openalex.org/W2326137140","https://openalex.org/W3196314919","https://openalex.org/W2963592743","https://openalex.org/W2044911123","https://openalex.org/W2061320783","https://openalex.org/W2952396616","https://openalex.org/W2966659947","https://openalex.org/W2963427894","https://openalex.org/W2059507721","https://openalex.org/W2160453969","https://openalex.org/W3104038630","https://openalex.org/W2141190339","https://openalex.org/W2324733037","https://openalex.org/W1967025884","https://openalex.org/W1992307797"],"abstract_inverted_index":{"The":[0,93],"Ulam":[1,36],"sequence":[2],"is":[3,54],"defined":[4],"as":[5,22,46],"a1":[6],"=":[7,10],"1,":[8],"a2":[9],"2,":[11],"and":[12,51,113],"an":[13],"being":[14],"the":[15,23,40,58,86,104],"smallest":[16],"integer":[17],"that":[18,38,77],"can":[19],"be":[20],"written":[21],"sum":[24],"of":[25,61,82,90,129,132],"two":[26],"distinct":[27],"earlier":[28],"elements":[29,89],"in":[30,126],"a":[31,62,71,80],"unique":[32],"way.":[33],"This":[34],"gives":[35],"remarked":[37],"understanding":[39],"sequence,":[41,92],"which":[42],"has":[43],"been":[44],"described":[45],"\u201cquite":[47],"erratic,\u201d":[48],"seems":[49,68,123],"difficult":[50],"indeed":[52],"nothing":[53],"known.":[55],"We":[56],"report":[57],"empirical":[59],"discovery":[60],"surprising":[63],"global":[64],"rigidity":[65],"phenomenon:":[66],"there":[67],"to":[69,124],"exist":[70],"real":[72],"\u03b1":[73],"\u223c":[74],"2.5714474995\u2026":[75],"such":[76],"supported":[78],"on":[79],"subset":[81],".":[83],"Indeed,":[84],"for":[85,97],"first":[87],"107":[88],"Ulam\u2019s":[91],"same":[94],"phenomenon":[95,122],"arises":[96],"some":[98],"other":[99,112],"initial":[100],"conditions":[101],"a1,":[102],"a2:":[103],"distribution":[105],"functions":[106],"look":[107],"very":[108],"different":[109],"from":[110],"each":[111],"have":[114],"curious":[115],"shapes.":[116],"A":[117],"similar":[118],"but":[119],"more":[120],"subtle":[121],"arise":[125],"Lagarias\u2019":[127],"variant":[128],"MacMahon\u2019s":[130],"\u201cprimes":[131],"measurement\u201d":[133],"sequence.":[134]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
