Base 124: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР

Color Key
OrangeFixed Pointnumber that becomes itself after one iteration
GreenFinal Numbersall numbers eventually reached, from all cycles
PurpleCycle Startiterations include entry into cycle, assuming it repeats
RedFull Cycleiterations include entire cycle, proving it repeats
BlueStart Numberssubset (optimization) of all numbers; minimal for full coverage
GrayNo Resultsany calculation that has no results

Digits # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
23 cycles50 nodes0М → Л1 → Й3 → Е7 → χF → ηV → yΒ → 2К → З5 → БB → οN → Οl → Sκ → Εv → 8Д → υH → γZ → qΚ → Iτ → αb → mΞ → Qμ → Ιr → Gφ → εX → uΖ → AВ → ρL → Τh → aβ → oΜ → Mπ → Ρj → Wζ → wΔ → 6Ж → ωD → λR → Ηt → CА → νP → Λp → Kς → Φf → eΧ → gΥ → cΩ → kΠ → Uθ → Αz
31 cycle (fixed) 1 node zМΑ
421 cycles5 nodesq3ИΛ → ЕJς8 → χΧdG → ηhΣW → yZβΓ
53 cycles4 nodesΦeМΦg → ΧdМΧf → ΨfМΥe → ΧgМΤf
612 cycles370 nodes62ММЙЗ → КЖ1К63 → ЙЗωC54 → ЕВμPA8 → χςΚpKG → ηΧJςeW → ΨygΤΒe → ic2ЙΩΤ → ЗlZβΟ6 → БqSιΚC → οΕIσvO → αΟ8Гlc → υmSιΞI → γΕQλva → Ιq8ГΚs → υJFφσI → ηγΨcZW → yrjΠΙΓ → WH3Иυη → ЕδxΒY8 → χt3ИΗG → ЕηCωV8 → χνyΑPG → ηΜ1КoW → ЙyMοΒ4 → ЕΡ2Йj8 → ЗχWεF6 → БθvΔUC → οΒ7ДyO → χΟ2ЙlG → ЗηSιV6 → БΕyΑvC → ο91КГO → ЙτΞlI4 → ЕβRκa8 → χΗoΛtG → ηMCωπW → νΣxΒiQ → ΛZ3Иγq → ЕrJςΙ8 → χΨGυdG → ηεiΡXW → yvXδΕΓ → u93ИГΗ → ЕτBАI8 → χοαaNG → ηΠnΜkW → yVNξηΓ → Οz3ИΑm → ЕS0Лκ8 → ЛχΕuF2 → Йθ9ВU4 → ЕσΑyJ8 → χΩ1КcG → ЙηkΟV4 → ЕzTθΑ8 → χΓ0ЛxG → Лη4ЗV2 → ЙГyΑ94 → Еτ1КI8 → ЙχαaF4 → ЕθnΜU8 → χΒNξyG → ηΟ2ЙlW → ЗySιΒ6 → БΕ2ЙvC → Зο8ГN6 → БυΟkHC → οδTθYO → ΟΓsΗxm → SE4Зψλ → ГκΖtSA → σΖBАuK → οΨAБdO → ρΟiΡlM → ΤYSιδi → ΕtZβΗw → qD7ДωΛ → χμJςQG → ηΨΙqdW → yjHτΡΓ → γX3Иεa → ЕvpΚΕ8 → χK8ГςG → υηΦeVI → γzfΥΑa → qe0ЛΧΛ → ЛhJςΤ2 → ЙΨaαd4 → ЕoiΡΜ8 → χYMοδG → ηΡsΗjW → yXDψεΓ → λv3ИΕS → ЕΗ8Гt8 → χυCωHG → νηγYVQ → ΛzrΘΑq → KG0Лφσ → ЛζΧdW2 → ЙxhΣΓ4 → Еa4Зβ8 → ГχoΛFA → σθLπUK → ΨΤΑyhe → ib1КαΤ → ЙnZβΝ4 → ЕqOνΚ8 → χΝIσnG → ηαOνbW → ΝymΝΒo → QO2Йξν → ЗΞΚpm6 → БRJςλC → οΨΗsdO → ΟjDψΡm → λXRκεS → ΘΖuΕut → EB9ВБω → σπκRMK → ΨΣΖtie → iZBАγΤ → οrZβΙO → ΟqGυΚm → εSIσκY → αΖtΖuc → mCAБАΟ → ρξRκOM → ΤΞΖtmi → aRBАλγ → οΘpΚsO → ΟKEχςm → ιΧRκeU → ΗΓgΤxu → cC4ЗАα → ГξlΞOA → σΞRκmK → ΨΗQλte → ΙiCωΣs → νZFφγQ → ηΛqΙpW → yLHτρΓ → γΥ3Иga → ЕqcΨΚ8 → χkIσΠG → ηαUηbW → ΑymΝΒΑ → Q2ММЙν → КμLπQ3 → ЗΤΙqh6 → БbHταC → ογmΝZO → ΟrPμΙm → ΛSGυκq → εΖJςuY → ΨuAБΖe → ρiAБΣM → ρΤYγhM → ΤsaαΘi → oaEχβΝ → ιpNξΛU → ΟΓKρxm → ΦS4Зκg → ГΖdΧuA → σiAБΣK → ρΨYγdM → ΤsiΡΘi → aYEχδγ → ιtpΚΗU → ΓKCωςy → νΧ3ИeQ → ЕΛgΤp8 → χcKρΩG → ηΦkΟfW → yfTθΦΓ → Γf3ИΦy → Еf3ИΦ8 → ЕχeΦF8 → χθfΥUG → ηΒdΧyW → yi2ЙΣΓ → ЗZ3Иγ6 → ЕБqΙB8 → χπHτMG → ηγΡiZW → yrXδΙΓ → uH3ИυΗ → ЕδBАY8 → χοsΗNG → ηΠDψkW → λyUηΒS → ΗΑ2Йzu → ЗC0ЛА6 → ЛБνOB2 → ЙπΜnM4 → ЕΣNξi8 → χΟYγlG → ηsSιΘW → ΕyEχΒw → ι82ЙДU → ЗφΒxG6 → Бζ3ИWC → ЕοwΓN8 → χΠ5ЖkG → БηUηVC → οΑyΑzO → Ο20ЛКm → ЛИRκ42 → ЙДΖt84 → ЕφBАG8 → χοεWNG → ηΠvΔkW → yV7ДηΓ → χz3ИΑG → Еη0ЛV8 → ЛχyΑF2 → Йθ1КU4 → ЙЕΑy74 → Еψ1КE8 → ЙχιSF4 → ЕθΔvU8 → χΒ7ДyG → χη2ЙVG → ЗηyΑV6 → Бz1КΑC → Йο0ЛN4 → ЛЕΟk72 → ЙψTθE4 → ЕκΒxS8 → χΖ3ИuG → ЕηAБV8 → χρyΑLG → ηΥ1КgW → ЙycΨΒ4 → Еk2ЙΠ8 → ЗχUηF6 → БθzzUC → οΑММyO → ξΒbΩyP → Νm2ЙΞo → ЗRNξλ6 → БΟΗslC → οTDψιO → λΟΓwlS → ΗT5Жιu → БΔBАwC → πξ6ЕON → ωΡΝmjE → λXPμεS → ΛΗuΕtq → KD9Вωσ → σμΧdQK → ΨΚhΣqe → iaIσβΤ → αpZβΛc → qmKρΞΛ → ΦRJςλg → ΨΘdΧse → jhEχΤΣ → ιbXδαU → ΓumΝΖy → QB3ИБν → ЕπΚpM8 → χΣJςiG → ηΨYγdW → ysiΡΘΓ → YF3Иχε → ЕθtΖU8 → χΒBАyG → οη2ЙVO → ЗΟyΑl6 → БT1КιC → ЙοΓwN4 → ЕΠ5Жk8 → БχUηFC → οθzzUO → ΟΑММym → ΞΒDψyn → λQ2ЙμS → ЗΚΖtq6 → БJBАσC → πξΨcON → ΡΞjΠmk → XVQληζ → ΙzvΔΑs → G80ЛДχ → ЛφζVG2 → ЙζxΒW4 → Еx3ИΓ8 → Еχ4ЗF8 → ГχηUFA → σθzzUK → ΨΑММye → ΧΒLπyf → Τg2ЙΥi → ЗdZβΨ6 → БqiΡΚC → οYIσδO → αΟsΗlc → mTDψιΟ → λΔRκwS → ΘΖ6Еut → ωEAБψE → ρλιSRM → ΤΘΔvsi → aF7Дχγ → χθpΚUG → ηΒJςyW → Ψy2ЙΒe → Зi2ЙΣ6 → ЗБYγB6 → БπrΘMC → οΣFφiO → ηΟYγlW → ysSιΘΓ → ΕF3Иχw → Еθ7ДU8 → ψφΑyGF → ιζ1КWU → ЙΓwΓx4 → Е64ЗЖ8 → ГАφFCA → σξζVOK → ΨΞxΒme → iR3ИλΤ → ЕΘZβs8 → χqEχΚG → ιηIσVU → αΓyΑxc → m51КЗΟ → ЙВRκA4 → ЕςΖtK8 → χΧBАeG → οηgΤVO → ΟzbΩΑm → mS0ЛκΟ → ЛΖRκu2 → ЙΗAБt4 → ЕρCωL8 → χνΤgPG → ηΜbΩoW → ymMοΞΓ → ΡR3Иλk → ЕΘVζs8 → χyEχΒG → ιη2ЙVU → ЗΓyΑx6 → Б51КЗC → ЙВξNA4 → ЕςΞlK8 → χΧRκeG → ηΗgΤtW → ycCωΩΓ → νl3ИΟQ → ЕΛSιp8 → χΕKρvG → ηΦ8ГfW → υyeΦΒI → γg2ЙΥa → ЗqcΨΚ6 → БkIσΠC → οαUηbO → ΟΑmΝzm → SQ0Лμλ → ЛΚΖtq2 → ЙJBАσ4 → ЕοΨcN8 → χΠjΠkG → ηWUηζW → ΑywΓΒΑ