Base 118: 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---
25 cycles2,808×(max) 24 nodes0Ж → Е1 → Г3 → ω7 → ρF → αV → sΒ → 8ψ → οH → ΦZ → kΚ → Oθ → Ηn → Iξ → Τb → gΞ → WΩ → qΔ → Cτ → ηP → Εp → Eς → γT → wx
2,808×(max) 24 nodes2Д → Б5 → υB → ιN → Ιl → Mκ → Λj → Qζ → Γr → Aφ → λL → Νh → Uβ → uz → 4В → χ9 → νJ → Ρd → cΣ → eΠ → aΥ → iΜ → Sδ → yv
468×4 nodes6А → σD → εR → Αt
468×4 nodesKμ → Οf → YΧ → mΘ
351×3 nodesGπ → ΨX → oΖ
31 cycle 280,722×(fixed) (max) 1 node wЖx
414 cycles614,559×(max) 29 nodesM9φλ → νΜhK → ΡTβe → wbΣy → g1ДΟ → ГXΧ4 → ωnΖ8 → ρHξG → αΥZW → sjΚΓ → Q9φη → νΔpK → ΡDςe → εbΣS → ΑfΞu → Y5АΨ → υnΖC → ιHξO → ΦΘla → kLκΛ → ΝPζi → ΕTβq → wDςy → ε1ДS → Гzt4 → ω5А8 → υπFC → ιΩVO → ΙrΒm
612,288×(max) 29 nodesgXΧΟ → oXΧΗ → oHξΗ → ΦHξa → ΦjΚa → kPζΛ → ΕPζq → ΕDςq → εDςS → εztS → Α5Аu → υ5АC → υθNC → ιΘlO → ΙLκm → ΝLκi → ΝTβi → wTβy → w1Дy → Г1Д4 → Гψ74 → ωπF8 → ρΩVG → αrΒW → s9φΓ → ν9φK → νΠdK → ΡbΣe → gbΣΟ
612,127×(max) 29 nodes61ДБ → ГτB4 → ωθN8 → ρΘlG → αLκW → ΝrΒi → U9φγ → νvxK → Ρ1Дe → ГbΣ4 → ωfΞ8 → ρXΧG → αnΖW → sHξΓ → Φ9φa → νjΚK → ΡPζe → ΕbΣq → gDςΟ → εXΧS → ΑnΖu → I5Аο → υΥZC → ιjΚO → ΙPζm → ΕLκq → ΝDςi → εTβS → Αvxu
607,820×(max) 29 nodesI9φο → νΥZK → ΡjΚe → cPζΤ → ΕfΞq → YDςΨ → εnΖS → ΑHξu → Φ5Аa → υjΚC → ιPζO → ΙΔpm → MDςλ → εΜhS → ΑTβu → w5Аy → υ1ДC → ГθN4 → ωΘl8 → ρLκG → αΜhW → sTβΓ → w9φy → ν1ДK → ГΠd4 → ωbΣ8 → ρfΞG → αXΧW → snΖΓ
607,562×(max) 29 nodesM1Дλ → ГΜh4 → ωTβ8 → ρvxG → α1ДW → ГrΒ4 → ω9φ8 → ρμJG → αΠdW → sbΣΓ → g9φΟ → νXΧK → ΡnΖe → cHξΤ → ΦfΞa → kXΧΛ → oPζΗ → ΕHξq → ΦDςa → εjΚS → ΑPζu → Ε5Аq → υDςC → ιδRO → Ιztm → M5Аλ → υΜhC → ιTβO → Ιvxm
606,864×(max) 29 nodesE1Дσ → ГδR4 → ωzt8 → ρ5АG → υΩVC → ιrΒO → Ι9φm → νLκK → ΡΜhe → cTβΤ → wfΞy → Y1ДΨ → ГnΖ4 → ωHξ8 → ρΥZG → αjΚW → sPζΓ → Ε9φq → νDςK → εΠdS → ΑbΣu → g5АΟ → υXΧC → ιnΖO → ΙHξm → ΦLκa → ΝjΚi → UPζγ → Εvxq
605,296×(max) 29 nodesQLκη → ΝΔpi → UDςγ → εvxS → Α1Дu → Г5А4 → ωτB8 → ρθNG → αΘlW → sLκΓ → Ν9φi → νTβK → Ρvxe → c1ДΤ → ГfΞ4 → ωXΧ8 → ρnΖG → αHξW → ΦrΒa → k9φΛ → νPζK → ΡΔpe → cDςΤ → εfΞS → ΑXΧu → o5АΗ → υHξC → ιΥZO → ΙjΚm
605,206×(max) 29 nodesQDςη → εΔpS → ΑDςu → ε5АS → υztC → ι5АO → υΘlC → ιLκO → ΝΘli → ULκγ → Νvxi → U1Дγ → Гvx4 → ω1Д8 → ГπF4 → ωΩV8 → ρrΒG → α9φW → νrΒK → Ρ9φe → νbΣK → ΡfΞe → cXΧΤ → ofΞΗ → YHξΨ → ΦnΖa → kHξΛ → ΦPζa → ΕjΚq
605,140×(max) 29 nodesIDςο → εΥZS → ΑjΚu → Q5Аη → υΔpC → ιDςO → εΘlS → ΑLκu → Ν5Аi → υTβC → ιvxO → Ι1Дm → ГLκ4 → ωΜh8 → ρTβG → αvxW → s1ДΓ → Г9φ4 → ωμJ8 → ρΠdG → αbΣW → sfΞΓ → Y9φΨ → νnΖK → ΡHξe → ΦbΣa → kfΞΛ → YPζΨ → ΕnΖq
604,476×(max) 29 nodesE5Аσ → υδRC → ιztO → Ι5Аm → υLκC → ιΜhO → ΙTβm → wLκy → Ν1Дi → ГTβ4 → ωvx8 → ρ1ДG → ГΩV4 → ωrΒ8 → ρ9φG → νΩVK → ΡrΒe → c9φΤ → νfΞK → ΡXΧe → obΣΗ → gHξΟ → ΦXΧa → ojΚΗ → QHξη → ΦΔpa → kDςΛ → εPζS → Εztq
604,082×(max) 29 nodesE9φσ → νδRK → Ρzte → c5АΤ → υfΞC → ιXΧO → ΙnΖm → MHξλ → ΦΜha → kTβΛ → wPζy → Ε1Дq → ГDς4 → ωδR8 → ρztG → α5АW → υrΒC → ι9φO → νΘlK → ΡLκe → ΝbΣi → gTβΟ → wXΧy → o1ДΗ → ГHξ4 → ωΥZ8 → ρjΚG → αPζW → ΕrΒq
604,036×(max) 29 nodesA1Дχ → ГμJ4 → ωΠd8 → ρbΣG → αfΞW → sXΧΓ → o9φΗ → νHξK → ΦΠda → kbΣΛ → gPζΟ → ΕXΧq → oDςΗ → εHξS → Φzta → k5АΛ → υPζC → ιΔpO → ΙDςm → εLκS → Νzti → U5Аγ → υvxC → ι1ДO → ГΘl4 → ωLκ8 → ρΜhG → αTβW → wrΒy
603,144×(max) 29 nodesI1Дο → ГΥZ4 → ωjΚ8 → ρPζG → αΔpW → sDςΓ → ε9φS → νztK → Ρ5Аe → υbΣC → ιfΞO → ΙXΧm → oLκΗ → ΝHξi → ΦTβa → wjΚy → Q1Дη → ГΔp4 → ωDς8 → ρδRG → αztW → s5АΓ → υ9φC → νθNK → ΡΘle → cLκΤ → ΝfΞi → YTβΨ → wnΖy
602,692×(max) 29 nodesA5Аχ → υμJC → ιΠdO → ΙbΣm → gLκΟ → ΝXΧi → oTβΗ → wHξy → Φ1Дa → ГjΚ4 → ωPζ8 → ρΔpG → αDςW → εrΒS → Α9φu → ν5АK → υΠdC → ιbΣO → ΙfΞm → YLκΨ → ΝnΖi → UHξγ → Φvxa → k1ДΛ → ГPζ4 → ωΔp8 → ρDςG → εΩVS → ΑrΒu
53 cycles137,957,064×3 nodesΡbЖΣe → ΤcЖΡc → ΣfЖΞd
69,316,782×(max) 4 nodesΡcЖΡe → ΣbЖΣd → ΤdЖΠc → ΣeЖΟd
14,040×2 nodesxvЖxx → xЖЖЖw
66 cycles3,682,487,176×(max) 188 nodesA86ωψχ → σπμJGE → εΩΠdWS → ΑrbΣΓu → gB5АυΟ → υκXΧMC → ιΜnΖiO → ΙTHξγm → ΦxLκwa → Νk0ЕΚi → ЕUOηβ2 → ГΗuyn4 → ωJ3Вν8 → ωρΡcF8 → ρβdΠUG → αvbΣyW → sg2ГΞΓ → БX9φΨ6 → υνoΕJC → ιΣFπcO → αΙeΟlW → saMιΥΓ → Λj9φΛk → νRPζεK → ΡΕΑspe → cF7ψρΤ → ρβfΞUG → αvXΧyW → so2ГΖΓ → БH9φο6 → υνΦYJC → ιΣlΘcO → ΙfLκΟm → ΝZLκΦi → ΝlTβΙi → wUMιβy → Λv1Дyk → ГQ2Гζ4 → БωΓq76 → υςBτEC → κθγSON → ΛΘxvmk → QL1Дλη → ГΞΔpg4 → ωXDςΨ8 → ρεoΕRG → αΒFπsW → αs8χΒW → οs8χΒI → οΦ8χZI → οΦkΙZI → ΦlNθΙa → ΙkMιΚm → ΛPLκηk → ΝΖPζoi → ΕUGοβq → ΨvDςyY → εo2ГΖS → БΑGοt6 → υΨ6ωXC → σιoΕNE → εΚFπkS → αΑOηtW → Ηs6ωΒo → σI8χξE → οεΤaRI → ΦΒhΜsa → kU8χβΛ → οvPζyI → ΦΕ2Гpa → БkEρΚ6 → υγOηTC → ιΗwwnO → ΙIЖЖνm → ξΘRδmJ → ΤΑKλtc → Οg6ωΞg → σYWΨΧE → εqmΗΔS → ΑKCσμu → ηΠ5АeQ → υΕaΤpC → ιiEρΜO → γΙSγlU → ywMιxw → Λ20ЕДk → ЕВPζ42 → ГψΔp84 → ωπDςG8 → ρεΨWRG → αΒpΔsW → sE8χςΓ → οδ9φSI → νΦyuZK → Ρl3ВΙe → ωcMιΣ8 → ρΛeΟjG → αaQεΥW → ΓsiΛΒs → SA8χφε → ομztKI → ΦΠ5Аea → υkaΤΚC → ιiOηΜO → ΙΗSγnm → yMIνκw → ΤΜ1Дic → ГgSγΞ4 → ωyWΨv8 → ρq2ГΔG → БαCσV6 → υηsΑPC → ιΖ7ψoO → ρΙGοlG → αΨMιXW → ΛsoΕΒk → QG8χπη → οΩΔpWI → ΦrDςΓa → εkAυΚS → λΑOηtM → ΝΗ6ωni → σUIνβE → εΤuybS → Αh3ВΝu → ωV5Аα8 → υρsΑFC → ιβ7ψUO → ρΙuylG → αN3ВιW → ωΚrΒk8 → ρP9φηG → ναΕoVK → ΡtFπΑe → αc6ωΣW → σseΟΒE → εa8χΥS → οΑiΛtI → ΦS6ωδa → σzjΚuE → εQ4БζS → χΔztqA → νD5АσK → υζΠdQC → ιΔbΣqO → ΙgCσΞm → ηXLκΨQ → ΝΕoΕpi → UGEρπγ → γΩvxWU → wr1ДΓy → ГB1Дυ4 → ГωιM74 → ωςΚjE8 → ρδPζSG → αΕyupW → sF3ВρΓ → ωβ9φU8 → ρνuyJG → αΣ3ВcW → ωseΟΒ8 → ρa8χΥG → οαiΛVI → ΦtRδΑa → Αk6ωΚu → σP5АηE → υεΕoRC → ιΒFπsO → αΙ8χlW → οsMιΒI → ΦΛ8χja → οkQεΚI → ΦΓOηra → ΗkAυΚo → λPHξηM → ΦΝΕoha → kVFπαΛ → αtPζΑW → Εs6ωΒq → σE8χςE → οεγSRI → ΦΒxvsa → k91ДχΛ → ГξPζI4 → ωΥΔpa8 → ρjDςΛG → εαQεVS → ΓΑsΑts
351,833,509×48 nodescOAυθΤ → λΘfΞmM → ΝYKλΧi → ΟnTβΗg → wYIνΧy → Τn1ДΗc → ГgIνΞ4 → ωΤWΨb8 → ρqgΝΔG → αWCσΩW → ηsqΓΒQ → ΕC8χτq → οθDςOI → εΦΗmZS → ΑlJμΙu → ΡN5Аιe → υΚbΣkC → ιgOηΞO → ΙΗWΨnm → qMIνκΕ → ΤΜDςic → εgSγΞS → ΑyWΨvu → q62ГАΕ → БτDςC6 → υθδROC → ιΘztmO → ΙL5Аλm → υΞLκgC → ιΝWΨhO → ΙqUαΔm → uMCσκΑ → ηΜ5АiQ → υΕSγpC → ιyEρvO → γΙ2ГlU → БwMιx6 → υΛ0ЕjC → ЕιQεN2 → ГΚΒrk4 → ωP9φη8 → ρνΕoJG → αΣFπcW → αseΟΒW → sa8χΥΓ → οj9φΛI → νΦQεZK → ΡΓkΙre
214,527,007×14 nodesiXPζΨΝ → ΕpTβΕq → wFDςρy → εβ1ДUS → ГΑuyt4 → ω73Вω8 → ωςπFE8 → ρδΩVSG → αzrΒuW → sA4БφΓ → χμ9φKA → ξμΟeKJ → ΤΠZΥec → kgaΤΞΛ
445,802×4 nodesεm6ωΘS → σΑKλtE → εΟ6ωfS → σΑYΦtE
106,930×(fixed) 1 node ΨoGοΖY
3,540×(fixed) 1 node xwЖЖwx
7+---Not showing digit sets 7+ due to verbosity.