{"id":"https://openalex.org/W7220955295","doi":"https://doi.org/10.48550/arxiv.2610.10095","title":"Making Every Number from 1 to N Under a Fixed Cycle of $+$, $\\times$, $-$, $\u00f7$","display_name":"Making Every Number from 1 to N Under a Fixed Cycle of $+$, $\\times$, $-$, $\u00f7$","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220955295","doi":"https://doi.org/10.48550/arxiv.2610.10095"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10095","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10095","pdf_url":"https://arxiv.org/pdf/2610.10095","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/2610.10095","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157974414","display_name":"Sean Lesmana","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lesmana, Sean","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5157988387","display_name":"Theodore Tjugiarto","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tjugiarto, Theodore","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.774399995803833,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.774399995803833,"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.06960000097751617,"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/T12504","display_name":"Mathematics and Applications","score":0.031099999323487282,"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/arithmetic-operations","display_name":"arithmetic operations","score":0.527999997138977},{"id":"https://openalex.org/keywords/combinatorial-number-theory","display_name":"combinatorial number theory","score":0.5009999871253967}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7124999761581421},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6736999750137329},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5906000137329102},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5859000086784363},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5274999737739563},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.5133000016212463},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4487000107765198},{"id":"https://openalex.org/C164680029","wikidata":"https://www.wikidata.org/wiki/Q1055293","display_name":"Multiple","level":2,"score":0.43950000405311584},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4318999946117401},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4088999927043915},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3928999900817871},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3610999882221222},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2655999958515167},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C90329073","wikidata":"https://www.wikidata.org/wiki/Q914232","display_name":"Ask price","level":2,"score":0.25690001249313354}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10095","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10095","pdf_url":"https://arxiv.org/pdf/2610.10095","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.2610.10095","doi":"https://doi.org/10.48550/arxiv.2610.10095","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10095","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:2610.10095","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10095","pdf_url":"https://arxiv.org/pdf/2610.10095","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/W7220955295.pdf","grobid_xml":"https://content.openalex.org/works/W7220955295.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2324476794","https://openalex.org/W1672410750","https://openalex.org/W2609117068","https://openalex.org/W4404385192","https://openalex.org/W2590818214","https://openalex.org/W2114773127","https://openalex.org/W1977215562","https://openalex.org/W4402770753","https://openalex.org/W2357920264","https://openalex.org/W2081708172"],"abstract_inverted_index":{"Start":[0],"with":[1],"the":[2,14,20,28,46,112,124],"number":[3],"$2$.":[4],"At":[5],"each":[6,51],"move,":[7],"combine":[8],"two":[9],"numbers":[10,47,93],"already":[11,43,94],"made,":[12],"but":[13],"operations":[15],"must":[16],"be":[17],"used":[18],"in":[19],"fixed":[21],"repeating":[22],"order":[23],"$+,\\times,-,\u00f7$.":[24],"We":[25,65],"ask":[26],"for":[27,73],"fewest":[29],"moves":[30,62,69,127],"needed":[31],"to":[32,38,103,128],"make":[33],"every":[34,74,130],"integer":[35],"from":[36],"$1$":[37],"$N$.":[39,132],"Since":[40],"$2$":[41],"is":[42,111],"one":[44,56],"of":[45],"we":[48,97,137],"want":[49],"and":[50,121],"move":[52],"makes":[53],"at":[54,59,106],"most":[55],"new":[57],"number,":[58],"least":[60],"$N-1$":[61,68],"are":[63,70],"needed.":[64],"show":[66],"that":[67,84,118],"also":[71],"enough":[72],"$N\\ge":[75],"9$.":[76],"Conventional":[77],"induction":[78],"cannot":[79],"work,":[80,120],"because":[81],"a":[82,88,99],"division":[83],"comes":[85],"right":[86],"after":[87],"completed":[89,100],"interval":[90,101],"$\\{1,\\dots,P\\}$":[91,102],"produces":[92],"made.":[95],"Instead":[96],"extend":[98],"$\\{1,\\dots,3P\\}$":[104],"all":[105],"once,":[107],"which":[108],"counting":[109],"shows":[110],"smallest":[113],"multiplicative":[114],"extension":[115],"$P\\to":[116],"kP$":[117],"can":[119],"then":[122],"adjust":[123],"last":[125],"few":[126],"reach":[129],"other":[131],"For":[133],"$9\\le":[134],"N\\le":[135],"33$":[136],"give":[138],"explicit":[139],"sequences,":[140],"found":[141],"by":[142],"computer":[143],"search.":[144]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-10-09T00:00:00"}
