{"id":"https://openalex.org/W7225640144","doi":"https://doi.org/10.5281/zenodo.24078012","title":"A083833 - palindromes p with 5p+1 palindrome: Branicky's conjectures C1/C2 proved (Lean 4)","display_name":"A083833 - palindromes p with 5p+1 palindrome: Branicky's conjectures C1/C2 proved (Lean 4)","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225640144","doi":"https://doi.org/10.5281/zenodo.24078012"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24078012","doi":"https://doi.org/10.5281/zenodo.24078012","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24078012","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24078012","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160353073","display_name":"Fr\u00e9d\u00e9ric Gaudin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gaudin, Frederic","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5160353073"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.4311999976634979,"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.4311999976634979,"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":0.15610000491142273,"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/T11567","display_name":"semigroups and automata theory","score":0.09189999848604202,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/palindromes","display_name":"palindromes","score":0.9150000214576721},{"id":"https://openalex.org/keywords/carry-chain","display_name":"carry chain","score":0.6919999718666077},{"id":"https://openalex.org/keywords/decimal-digits","display_name":"decimal digits","score":0.421999990940094},{"id":"https://openalex.org/keywords/repunits","display_name":"repunits","score":0.5920000076293945},{"id":"https://openalex.org/keywords/lean-4-formal-proof","display_name":"Lean 4 formal proof","score":0.6039999723434448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8614000082015991},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6165000200271606},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5954999923706055},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.527400016784668},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.48350000381469727},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47360000014305115},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4700999855995178},{"id":"https://openalex.org/C44667518","wikidata":"https://www.wikidata.org/wiki/Q12321","display_name":"Palindrome","level":4,"score":0.4666999876499176},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.4474000036716461},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.4343999922275543},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.4138999879360199},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.38510000705718994},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3490000069141388},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.27959999442100525}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.5281/zenodo.24078012","doi":"https://doi.org/10.5281/zenodo.24078012","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24078012","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.24078013","doi":"https://doi.org/10.5281/zenodo.24078013","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24078013","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.24083223","doi":"https://doi.org/10.5281/zenodo.24083223","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24083223","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.24084453","doi":"https://doi.org/10.5281/zenodo.24084453","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24084453","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.24085389","doi":"https://doi.org/10.5281/zenodo.24085389","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24085389","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.24086039","doi":"https://doi.org/10.5281/zenodo.24086039","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24086039","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.24088119","doi":"https://doi.org/10.5281/zenodo.24088119","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24088119","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24078012","doi":"https://doi.org/10.5281/zenodo.24078012","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24078012","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":null,"license_id":null,"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W7225111083"],"related_works":["https://openalex.org/W4226278886","https://openalex.org/W7106845267","https://openalex.org/W7106341365","https://openalex.org/W7105859165","https://openalex.org/W7148857843","https://openalex.org/W7116124229","https://openalex.org/W4409343890","https://openalex.org/W7221774892","https://openalex.org/W2285442814","https://openalex.org/W2589610593"],"abstract_inverted_index":{"theorems":[0,189],"A083833_C1":[1],"/":[2],"A083833_C2":[3],"(unconditional,":[4],"standard":[5,231],"axioms":[6,232],"only),":[7],"proved":[8,109,116],"in":[9,110,173,191,197],"the":[10,52,61,66,92,122,125,145,166,187,198,204,210,218],"carry-chain":[11],"module":[12,163],"A083833.lean":[13],"(multiplier":[14],"5):":[15],"for":[16,118,181],"every":[17,39,74],"palindrome":[18,34],"p":[19,42,70,77,81,155],"with":[20,95,104],"m":[21,68,136],">=":[22],"1":[23,105],"decimal":[24],"digits":[25,62,97],"such":[26],"that":[27],"q":[28,158,172,178],"=":[29,82,129,139,149,156,159,179],"5p+1":[30],"is":[31,43,71,98],"also":[32,164],"a":[33],"(of":[35],"m'":[36],"digits),":[37],"(C1)":[38],"digit":[40,75,120],"of":[41,69,76,171,203,209,213,217,222],"<=":[44],"3":[45],"-":[46,84,186],"Branicky's":[47,85],"first":[48],"'(Conjectures)'":[49],"item":[50],"on":[51],"OEIS":[53,182],"entry":[54],"(Jun":[55],"2021:":[56],"'All":[57],"terms":[58,102],"contain":[59],"only":[60,93,233],"{0,1,2,3}');":[63],"(C2)":[64],"if":[65],"length":[67],"EVEN":[72],"then":[73],"equals":[78],"2,":[79],"i.e.":[80],"22...2":[83],"second":[86],"conjecture":[87],"verbatim":[88],"('For":[89],"d":[90,96],"even,":[91],"term":[94],"2^d;":[99],"equivalently,":[100],"all":[101,119],"starting":[103],"have":[106],"odd":[107],"length'),":[108],"its":[111],"full":[112],"strong":[113],"form.":[114],"Both":[115],"here":[117],"lengths;":[121],"proof":[123],"distinguishes":[124],"same-length":[126],"case":[127,147],"(m'":[128,148],"m:":[130],"symmetric":[131],"2-periodic":[132],"carry":[133,152],"chain":[134,153],"forcing":[135,154],"odd,":[137],"a_0":[138],"1,":[140],"alternating":[141],"classes":[142],"{0,1}/{2,3})":[143],"from":[144],"overflow":[146],"m+1:":[150],"constant":[151],"22...2,":[157],"11...1).":[160],"The":[161],"shared":[162],"proves":[165],"image-sequence":[167],"conjectures":[168],"A083834_C1":[169],"(digits":[170],"{0,1,5,6})":[174],"and":[175,224],"A083834_C2":[176],"(even-length":[177],"repunit)":[180],"A083834,":[183],"packaged":[184],"separately":[185],"companion":[188],"ship":[190],"this":[192],"repository":[193],"since":[194],"they":[195],"live":[196],"same":[199],"module.":[200],"Universal":[201],"properties":[202],"members,":[205],"NOT":[206],"an":[207],"enumeration":[208],"sequence:":[211],"membership":[212],"specific":[214],"values,":[215],"completeness":[216],"published":[219],"list,":[220],"existence":[221],"members":[223],"finitude":[225],"are":[226],"not":[227],"claimed.":[228],"Trust":[229],"base:":[230],"[propext,":[234],"Classical.choice,":[235],"Quot.sound]":[236],"expected;":[237],"zero":[238,240],"sorry,":[239],"native_decide.":[241]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
