Base 105: Maximum Iteration Sequences: Full Cycle

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
Full Cycle
12 max steps100
229 max steps10 → 0σ → ς1 → π3μ7δFΜVzhΘZjxΠRntθBΥNvlΩJΔdrpπ3
355 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 → qσqpσrqσq
416 max stepsr000 → qσσq → qpqr → 1σσς → ς0ς2ςο32πλ74μγF8δΛVGΜeΒWfMΥΓxMΥkxCζkΣCζQΣqpQr0ςqς0ς2
544 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 → ΙYσΘZΙYσΘZ
6522 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 → fL9ιΧΓΩΑMΥgKΔxJΨjeΔPDεΣeΠsOΣoStn3οtoμ64ξν8κηγFCAΩΤΛVOKΔueΒmePN7λΥΤδwsnkGΜC4ξηWκΤeΒOAΩuMΥmKΔx7λjeδPDεΣGΠΜroVSng2πΑuξK6μΨ6θζΒeDCΥΡMΥQOxvpqlkDA0ςιηςΨΡPK2πΓqpe4μO0ςΤ8ςδtmF2πΝ6μU4μζhyD8δΡGβQGΜΚpqXWfc0ςΕΓςSMΥΟ2πxluj4μE8κε8δβΞSHGΜΙkvYWfaAθΗΓΧWMΥΛMzxdΓjiPHDεβΤΠΙsnYSna4ξΗuκW6μΛAζΩdΓJEΠΕOΣcStnRΟton64ξνuκη6μCAζΩΣOJEΠΕsncSnS4ξΟuκm6μuAζΩ7λJEδΠΔcRGΜoQΠsWpf3οΒsμM2πΦ8ξδxiF6θΝEδUCΥΞhyTOvkGβwmΚC8κηYβΤaΖOIΘuUΜmahX7λΚΑδcIΩΕGΜΖRΟbWnfTΝΒujM6μΦyζyEδiEΠΞFγTSΜnjwtWfD5νζΓθΡMΥQCΥxpqjOvE0ςεmςΟ8κS2πβluH4μΙ8κY8δβZΗHGΜΙWΚYWfdZΗΔΓXQMΥΡΛxqcΔqkRCσσζΡηΠCζRDΤΡnsQPtq4ξqoκ4σσξAοι3οA5μκΧK98δαΑfIGΜΗKΧaWΒfVΛΒgfMKΧΦΓΒyMΥigxLFγΧkΜΑCζgWΣfJΨΒQΔrLΦpezP1ρΣiπsGβo4μΚ3οX8μδbΕF8δΝSΞUGΜlhyvWfH9ιβΓΩΙMΥYKΔxZΗjeXPDεΣΛΠscΔoSnR3οΠuμo6μs8ζδ3οFEμΠΜUR8δogzsGΜJ3οΩWμΕeΒc8δSMΥΟGΜxlujWfE8κεΓβΟMΥSIΘxlujaXE8κεΛβΟcΔSIΘmQΠuapX7λΚsδc2πΕGξΜRΟV6θnfΑtCΥL5νΧOθΑulgCΥK8κΨOβΓuleIΘO8κΤaβuWΚmIΘd7λΔaδXPΡΚGΜrbΕpWfT1ρΞΓπkMΥw4μxBηj8δΥDεNGΠΜvkVSngAθΑuΧK6μΨMζΓyheEΠOGβΤSΚumtmYb86μλΗζγUΜGEΠΛgzWSneIΩΓuΖO6μΤcζuSΞmEΠl7λvSδn9ιtGΩΜ5νVKθΔfΑdCΥQKΧΡOΒvpqlgLA0ςιΨςΨΑfK2πΓKΧe4μΒNΤf8δvLΦlGΜz9ιhWΩfHαΒKΘΔLΦdazXPΡΚircGβΕqΚS0ςΟYςmaΖu2πV7λΜ4μδfΑF8δΝKΧUGΜΒhyfWfMGβΦΓΚyMΥiYxbFγΖkΜUCζΝWΣieΒyQrNFγΥqΜw0ςkWςfBηΒ2πΥLΦN4μzvkh8δIAθαGΧΜΖaVMzgUΜΑihKGβΨΑΚΓIΩeYΖbNΤΖcvUSΞΝmli8κywβGAθγIΧΛΗZWMzeWΚΓidOGβΤΕΚuQΠmYpb7λΖsδU2πΝGξΜhyV6θgGβΑCΥΚJΨXOΔvbΕleTP9ιΣΟΩskvoKΔB3οθeμΦOΣM8δysniGΜG4ξγWκΛeΒWAΩeMΥΓKΔxNΤjevPDεΣmΠs8κoSβn3οtIμΘ5νZ8θδXΙFCΥΝaΖUOviUΜymhG8κγΑβΛIΩWIΘΖdΓbaXUOΣΝΛticΔyoRG4ξγΡκΛorWAΩe2πΓKξΔNΤd6θvPΡlCΥr9ιpOΩv1ρlKπΔ9ιd4μΩPΡJ8δΕqpcGΜS0ςΟWςmeΒu2πN7λΥ4μδvkF8δΝAθUGΧΜhyVMzgGβΑiΚKGβΨYΚΓaΖeYbVNΤΜΗvgUΜΑmhK8κΨΑβΓIΩeIΘΖNΤbavXTΝΚmjc8κΕyβSEδΟIΞΘluZUjY8κΙyβaEδΗIΞΘVΛZUjfXΙΒybMEδΦΗΞyUΜiUjhFγzyΜIEδαWΞΗeΒaUjWMΥΛyxeEδΓkΞOCζΤUΣuixmQrF7λδqδΝ0ςUGςΜhyV2πgGβΑ4μΚJΨX8δΔbΕdGΜTPΡΞWrkeΒwqNC0ςηΦςΤwjO2πuCζm4μΣ7λP8εγroGFΞΛ2πWUξjdΓx6θPDεΣCΥΠroROvo2πsmξ93οκ6μθΩIB8δΦΕbMGΜySΞiWlfFγΒwΜMAθΦWΧyeΒiMzNFγΥiΜwGβkWΚfBηΒYΥbLΦΖOzvTΝlijH9ιβyΩΙEδYKΞΔZΗdUjXPΡΚyrcEδΕqΞS0ςΟUςmixu2πF7λδ4μδΜUF8δΝgzUGΜiIΩyWΖfFγΒcΜTLΦΞWzkeΒwiNHBηβΦΥΙwjYOvaCζΗmΣW8κΛQβrdΓpIΘP1ρΣaπsWΚo4μd3οΔ8μδPΡF8δΝqpUGΜi0ςyWςfFγΒ2πΜLΦV4μzfΑh8δLHαΧGΜΘzgZWfYIΩΙΓΖaMΥΗcxWSΞΛkleCζΓwΣOAθΤQΧuqpmMz80ςλiςγGβG2πΛΙXW4μeaΖΓ8δVNΤΜGΜvfΑlWfL9ιΧΓ