Base 105: Maximum Iteration Sequences: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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 Max Steps Max Step Example
Cycle Start
11 max steps10
23 max steps10 → 0σ → ς1 → π3
353 max steps100 → 0σσ → ςσ1 → ρσ2 → πσ3 → οσ4 → ξσ5 → νσ6 → μσ7 → λσ8 → κσ9 → ισA → θσB → ησC → ζσD → εσE → δσF → γσG → βσH → ασI → ΩσJ → ΨσK → ΧσL → ΦσM → ΥσN → ΤσO → ΣσP → ΡσQ → ΠσR → ΟσS → ΞσT → ΝσU → ΜσV → ΛσW → ΚσX → ΙσY → ΘσZ → Ησa → Ζσb → Εσc → Δσd → Γσe → Βσf → Ασg → zσh → yσi → xσj → wσk → vσl → uσm → tσn → sσo → rσp → qσq
44 max stepsr000 → qσσq → qpqr → 1σσς → ς0ς2
543 max steps30000 → 2σσσρ → ρ1σρ3 → ςνσ52 → ρμσ63 → πκσ84 → οησB5 → ξγσF6 → νΧσK7 → μΠσQ8 → λΙσX9 → κΑσfA → ιrσoB → θhσyC → ηnσsD → ζgσzE → εmσtF → δfσΑG → γlσuH → βeσΒI → αkσvJ → ΩdσΓK → ΨjσwL → ΧcσΔM → ΦiσxN → ΥbσΕO → ΤhσyP → ΣaσΖQ → ΡgσzR → ΠZσΗS → ΟfσΑT → ΞYσΘU → ΝeσΒV → ΜXσΙW → ΛdσΓX → ΚWσΚY → ΛaσΖX → ΚZσΗY → ΙZσΗZ → ΘYσΘa → ΙWσΚZ → ΛZσΗX → ΚaσΖY → ΙYσΘZ
6180 max stepsN000Vl → lVMΥΜw → xgAθΑk → ΧKCζΨM → ΣΓyheQ → rOGβΤq → Κu0ςmY → ςb7λΖ2 → πδTΝF4 → μΝixU8 → δiEδyG → ΞΜFγVU → ΜjfΑxW → fLDεΧΓ → ΠΑMΥgS → xnJΨtk → ΔD5νζe → θΡOΣQC → ΥtpqnO → v60ςνm → ςη8κC2 → πβΣOH4 → μΙsnY8 → δa4ξΗG → κΜVΛVA → ΩgeΒΑK → ΔNJΨΥe → ΔwOΣke → tPBηΣo → Υs4ξoO → κv3οlA → μΩ9ιJ8 → δΩΔcJG → ΜΕQΠcW → pfRΟΒs → nM2πΦu → ξy6μi6 → θζFγDC → ΥΡΛVQO → vqeΒqm → N8σσκΦ → λΥCζN9 → βΣvkPI → ΘsAθoa → ΧX3οΚM → μzbΕh8 → δTHαΞG → ΜΘjwZW → fYCζΙΓ → ΣaMΥΗQ → xrVΛpk → fD1ρζΓ → πΡMΥQ4 → μxpqj8 → δE0ςεG → ςΟΛVS2 → πmeΒu4 → μN7λΥ8 → εγvkGF → ΞΛAθWU → ΧjdΓxM → zPDεΣi → ΠsGβoS → Κn3οtY → μb5νΖ8 → θδTΝFC → ΥΝixUO → viEδym → ΞG8κγU → βΛixWI → ΘeEδΓa → ΞXNΤΚU → vjbΕxm → TE8κεΟ → βΟkvSI → ΘmAθua → ΧX7λΚM → δzbΕhG → ΜTHαΞW → ΘkeΒwa → XNBηΥΛ → ΥwcΔkO → vRBηΠm → Υo8κsO → βv3οlI → μΘ9ιZ8 → δΩXΙJG → ΜΕaΖcW → fVRΟΜΓ → ngMΥΑu → xK6μΨk → ζΓCζeE → ΣΠNΤRQ → vrnspm → 951ρξλ → πιαHA4 → μΨΗZK8 → δΓWΚeG → ΜdNΤΔW → vfPΡΒm → rM8κΦq → βy0ςiI → ςΘFγZ2 → πΜXΙV4 → μgaΖΑ8 → δVJΨΜG → ΜΔfΑdW → fQKΧΡΓ → ΒqMΥqg → xKσσΧk → ΨwNΤkL → ΒvBηlg → ΥL9ιΧO → ΩΑulgK → ΔK8κΨe → βΓOΣeI → ΘtNΤna → vX5νΚm → θc8κΕC → βΥRΟNI → Θwmtka → XC6μηΛ → ζΤcΔOE → ΠuQΠmS → pn7λts → δ62πνG → ξηΛVC6 → θΤeΒOC → ΥuMΥmO → xv7λlk → δD9ιζG → ΩΡΛVQK → ΔqeΒqe → PMσσΥΤ → ΦΣ0ςPN → ςxroj2 → πE2πε4 → ξμΞS76 → θεkvEC → ΥΟAθSO → ΧvlulM → zA8κιi → βΨGβKI → ΚΘΒeZY → bYMΥΙΗ → xaUΜΗk → hWCζΛΑ → ΣeIΩΓQ → ΖrNΤpc → vT1ρΞm → πk8κw4 → μβBηH8 → δΥΘYNG → ΜwYΘkW → fZBηΘΓ → ΥYMΥΙO → xvZΗlk → XD9ιζΛ → ΩΡcΔQK → ΔqQΠqe → pOσσΣs → ΤrOΣpP → us1ρon → π73ομ4 → νλδE87 → ζγΝTGE → ΠΛixWS → neEδΓu → ΞO6μΤU → ζuixmE → ΠF7λδS → δΝmtUG → Μi6μyW → ζfFγΒE → ΠΜLΦVS → znfΑti → LH5νβΨ → θΙΑfYC → ΥaKΧΗO → ΒvVΛlg → fL9ιΧΓ