Base 124: Cycles Sequences: All Cycle Counts

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)
Frequency Cycle
Length
Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
23 cycles6,150×(max) 50 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
1,230×10 nodes4И → Г9 → σJ → Ψd → iΣ → Yδ → sΘ → Eψ → ιT → Γx
246×2 nodesOξ → Νn
31 cycle 325,376×(fixed) (max) 1 node zМΑ
421 cycles650,549×(max) 5 nodesC3ИБ → ЕξN8 → χΞlG → ηRκW → ΗxΒu
621,762×(max) 5 nodesKBАσ → οΧdO → ΟhΣm → aRκγ → ΗpΚu
538,494×(max) 5 nodesS3Иλ → ЕΖt8 → χBАG → οζVO → ΟxΒm
524,700×(max) 5 nodesy3ИΓ → Е3И8 → ЕφF8 → χζVG → ηxΒW
521,538×(max) 5 nodesiZβΤ → qZβΛ → qJςΛ → ΨJςe → ΨhΣe
521,442×(max) 5 nodesa3Иγ → ЕpΚ8 → χJςG → ηΧdW → yhΣΓ
521,198×(max) 5 nodesSBАλ → οΖtO → ΟBАm → οRκO → ΟΖtm
520,202×(max) 5 nodesyRκΓ → Η3Иu → ЕBА8 → χξNG → ηΞlW
519,838×(max) 5 nodesK3Иσ → ЕΧd8 → χhΣG → ηZβW → ypΚΓ
519,610×(max) 5 nodesSJςλ → ΨΖte → iBАΤ → οZβO → ΟpΚm
515,784×(max) 5 nodesiRκΤ → ΗZβu → qBАΛ → οJςO → ΨΞle
513,180×(max) 5 nodesaJςγ → ΨpΚe → iJςΤ → ΨZβe → qhΣΛ
429,324×(max) 5 nodesyJςΓ → Ψ3Иe → ЕhΣ8 → χZβG → ηpΚW
429,292×(max) 5 nodesΟ3Иm → ЕRκ8 → χΖtG → ηBАW → οxΒO
427,420×(max) 5 nodesqRκΛ → ΗJςu → ΨBАe → οhΣO → ΟZβm
427,388×(max) 5 nodesΗBАu → οBАO → οΞlO → ΟRκm → ΗRκu
427,356×(max) 5 nodesi3ИΤ → ЕZβ8 → χpΚG → ηJςW → ΨxΒe
427,324×(max) 5 nodesyBАΓ → ο3ИO → ЕΞl8 → χRκG → ηΖtW
427,260×(max) 5 nodesη3ИW → ЕxΒ8 → χ3ИG → ЕζV8 → χxΒG
425,452×(max) 5 nodesaBАγ → οpΚO → ΟJςm → ΨRκe → ΗhΣu
425,388×(max) 5 nodesq3ИΛ → ЕJς8 → χΧdG → ηhΣW → yZβΓ
53 cycles176,214,782×3 nodesΦdМΧg → ΨeМΦe → ΧhМΣf
88,335,996×(max) 4 nodesΦeМΦg → ΧdМΧf → ΨfМΥe → ΧgМΤf
15,498×2 nodesΑyМΑΑ → ΑМММz
612 cycles2,512,065,306×104 nodesIC2ЙАυ → ЗξβZO6 → БΞpΚmC → οRJςλO → ΨΟΗsle → iTDψιΤ → λΔZβwS → Ηq6ЕΚu → ωJBАσE → ολΨcRO → ΟΘjΠsm → WSEχκη → ιΖxΒuU → ΓB3ИБy → Еπ3ИM8 → ЕχΡiF8 → χθXδUG → ηΒtΖyW → yC2ЙАΓ → Зξ3ИO6 → ЕБΝmB8 → χπPμMG → ηΣΚpiW → yZJςγΓ → Ψr3ИΙe → ЕiGυΣ8 → χεYγXG → ηvrΘΕW → yG8ГφΓ → υζ3ИWI → ЕγwΓZ8 → χr5ЖΙG → БηGυVC → οεyΑXO → Οv1КΕm → ЙS8Гκ4 → ЕυΕuH8 → χδ9ВYG → σηsΗVK → ΨzDψΑe → λi0ЛΣS → ЛΗYγt2 → ЙsCωΘ4 → ЕνEχP8 → χιΛoTG → ηΔLπwW → Τy6ЕΒi → ωa2ЙβE → ЗλoΛR6 → БΘLπsC → οΤEχhO → ιΟaαlU → ΓoSιΜy → ΕN3Иοw → ЕΠ7Дk8 → ψφUηGF → ιζzzWU → ΓwММΓy → ΔΑММyx → ΓΒ2Йyy → З42ЙИ6 → ЗДАB86 → БφξNGC → οζΞlWO → ΟxRκΓm → ΗS4Зκu → ГΖBАuA → σοAБNK → ρΨΟkdM → ΤjTθΡi → ΓaWεβy → wp3ИΛΕ → ЕL7Дρ8 → ψφΤgGF → ιζbΩWU → ΓxlΞΓy → S53ИЗλ → ЕВΖtA8 → χςBАKG → οηΦeVO → ΟzfΥΑm → eS0ЛκΨ → ЛΖhΣu2 → ЙaAБβ4 → ЕρoΛL8 → χΥLπgG → ηΤcΨhW → ykaαΠΓ → oV3ИηΝ → ЕzNξΑ8 → χΟ0ЛlG → ЛηSιV2 → ЙΕyΑv4 → Е91КГ8 → ЙχσIF4 → ЕθΩbU8 → χΒlΞyG → ηS2ЙκW → ЗΖxΒu6 → БB3ИБC → ЕπξNM8 → χΣΞliG → ηZRκγW → ΗyqΙΒu
2,202,117,156×(max) 370 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
838,512,408×6 nodeseTDψιΨ → λΔhΣwS → Ηa6Еβu → ωpBАΛE → ολKρRO → ΦΟΗslg
102,753,995×16 nodesηΘ1КsW → ЙyEχΒ4 → Еι2ЙT8 → ЗχΓwF6 → Бθ5ЖUC → БοΑyNC → οΠ1КkO → ЙΟUηl4 → ЕΑSιz8 → χΕ0ЛvG → Лη8ГV2 → ЙυyΑH4 → Еδ1КY8 → ЙχsΗF4 → ЕθDψU8 → χλΑyRG
16,976,664×32 nodesχr1КΙG → ЙηGυV4 → ЕεyΑX8 → χv1КΕG → Йη8ГV4 → ЕυyΑH8 → χδ1КYG → ЙηsΗV4 → ЕzDψΑ8 → χλ0ЛRG → ЛηΗsV2 → ЙzDψΑ4 → Еλ0ЛR8 → ЛχΗsF2 → ЙθDψU4 → ЕλΑyR8 → χΘ1КsG → ЙηEχV4 → ЕιyΑT8 → χΔ1КwG → Йη6ЕV4 → ЕωyΑD8 → χμ1КQG → ЙηΙqV4 → ЕzHτΑ8 → χγ0ЛZG → ЛηqΙV2 → ЙzHτΑ4 → Еγ0ЛZ8 → ЛχqΙF2 → ЙθHτU4 → ЕγΑyZ8
3,938,020×6 nodesοT1КιO → ЙΟΓwl4 → ЕT5Жι8 → БχΓwFC → οθ5ЖUO → БΟΑylC
3,351,658×10 nodesmc4ЗΩΟ → ГlRκΟA → σΗSιtK → ΨΕCωve → νi8ГΣQ → υΛYγpI → γsKρΘa → ΦqEχΚg → ιeIσΧU → αΓgΤxc
3,350,332×2 nodesοT5ЖιO → БΟΓwlC
2,219,633×2 nodeseaKρβΨ → ΦphΣΛg
2,218,152×6 nodesοθ1КUO → ЙΟΑyl4 → ЕT1Кι8 → ЙχΓwF4 → Еθ5ЖU8 → БχΑyFC
670,246×2 nodesЕθ1КU8 → ЙχΑyF4
3,906×(fixed) 1 node ΑzММzΑ
7+---Not showing digit sets 7+ due to verbosity.