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 steps1 → 0 → 0
229 max steps10 → 0σ → ς1 → π3 → μ7 → δF → ΜV → fΒ → LΧ → zh → Hβ → ΘZ → XΚ → bΖ → TΞ → jx → Dζ → ΠR → nt → 5ξ → θB → ΥN → vl → 9κ → ΩJ → Δd → PΣ → rp → 1ς → π3
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 → qσq → pσr → qσq
416 max stepsr000 → qσσq → qpqr → 1σσς → ς0ς2 → ςο32 → πλ74 → μγF8 → δΛVG → ΜeΒW → fMΥΓ → xMΥk → xCζk → ΣCζQ → ΣqpQ → r0ςq → ς0ς2
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 → ΙYσΘZ → ΙYσΘZ
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 → fL9ιΧΓ → ΩΑMΥgK → ΔxJΨje → ΔPDεΣe → ΠsOΣoS → tn3οto → μ64ξν8 → κηγFCA → ΩΤΛVOK → ΔueΒme → PN7λΥΤ → δwsnkG → ΜC4ξηW → κΤeΒOA → ΩuMΥmK → Δx7λje → δPDεΣG → ΠΜroVS → ng2πΑu → ξK6μΨ6 → θζΒeDC → ΥΡMΥQO → xvpqlk → DA0ςιη → ςΨΡPK2 → πΓqpe4 → μO0ςΤ8 → ςδtmF2 → πΝ6μU4 → μζhyD8 → δΡGβQG → ΜΚpqXW → fc0ςΕΓ → ςSMΥΟ2 → πxluj4 → μE8κε8 → δβΞSHG → ΜΙkvYW → faAθΗΓ → ΧWMΥΛM → zxdΓji → PHDεβΤ → ΠΙsnYS → na4ξΗu → κW6μΛA → ζΩdΓJE → ΠΕOΣcS → tnRΟto → n64ξνu → κη6μCA → ζΩΣOJE → ΠΕsncS → nS4ξΟu → κm6μuA → ζΩ7λJE → δΠΔcRG → ΜoQΠsW → pf3οΒs → μM2πΦ8 → ξδxiF6 → θΝEδUC → ΥΞhyTO → vkGβwm → ΚC8κηY → βΤaΖOI → ΘuUΜma → hX7λΚΑ → δcIΩΕG → ΜΖRΟbW → nfTΝΒu → jM6μΦy → ζyEδiE → ΠΞFγTS → ΜnjwtW → fD5νζΓ → θΡMΥQC → ΥxpqjO → vE0ςεm → ςΟ8κS2 → πβluH4 → μΙ8κY8 → δβZΗHG → ΜΙWΚYW → fdZΗΔΓ → XQMΥΡΛ → xqcΔqk → RCσσζΡ → ηΠCζRD → ΤΡnsQP → tq4ξqo → κ4σσξA → οι3οA5 → μκΧK98 → δαΑfIG → ΜΗKΧaW → ΒfVΛΒg → fMKΧΦΓ → ΒyMΥig → xLFγΧk → ΜΑCζgW → ΣfJΨΒQ → ΔrLΦpe → zP1ρΣi → πsGβo4 → μΚ3οX8 → μδbΕF8 → δΝSΞUG → ΜlhyvW → fH9ιβΓ → ΩΙMΥYK → ΔxZΗje → XPDεΣΛ → ΠscΔoS → nR3οΠu → μo6μs8 → ζδ3οFE → μΠΜUR8 → δogzsG → ΜJ3οΩW → μΕeΒc8 → δSMΥΟG → ΜxlujW → fE8κεΓ → βΟMΥSI → Θxluja → XE8κεΛ → βΟcΔSI → ΘmQΠua → pX7λΚs → δc2πΕG → ξΜRΟV6 → θnfΑtC → ΥL5νΧO → θΑulgC → ΥK8κΨO → βΓuleI → ΘO8κΤa → βuWΚmI → Θd7λΔa → δXPΡΚG → ΜrbΕpW → fT1ρΞΓ → πkMΥw4 → μxBηj8 → δΥDεNG → ΠΜvkVS → ngAθΑu → ΧK6μΨM → ζΓyheE → ΠOGβΤS → ΚumtmY → b86μλΗ → ζγUΜGE → ΠΛgzWS → neIΩΓu → ΖO6μΤc → ζuSΞmE → Πl7λvS → δn9ιtG → ΩΜ5νVK → θΔfΑdC → ΥQKΧΡO → Βvpqlg → LA0ςιΨ → ςΨΑfK2 → πΓKΧe4 → μΒNΤf8 → δvLΦlG → Μz9ιhW → ΩfHαΒK → ΘΔLΦda → zXPΡΚi → rcGβΕq → ΚS0ςΟY → ςmaΖu2 → πV7λΜ4 → μδfΑF8 → δΝKΧUG → ΜΒhyfW → fMGβΦΓ → ΚyMΥiY → xbFγΖk → ΜUCζΝW → ΣieΒyQ → rNFγΥq → Μw0ςkW → ςfBηΒ2 → πΥLΦN4 → μzvkh8 → δIAθαG → ΧΜΖaVM → zgUΜΑi → hKGβΨΑ → ΚΓIΩeY → ΖbNΤΖc → vUSΞΝm → li8κyw → βGAθγI → ΧΛΗZWM → zeWΚΓi → dOGβΤΕ → ΚuQΠmY → pb7λΖs → δU2πΝG → ξΜhyV6 → θgGβΑC → ΥΚJΨXO → ΔvbΕle → TP9ιΣΟ → ΩskvoK → ΔB3οθe → μΦOΣM8 → δysniG → ΜG4ξγW → κΛeΒWA → ΩeMΥΓK → ΔxNΤje → vPDεΣm → Πs8κoS → βn3οtI → μΘ5νZ8 → θδXΙFC → ΥΝaΖUO → viUΜym → hG8κγΑ → βΛIΩWI → ΘΖdΓba → XUOΣΝΛ → ticΔyo → RG4ξγΡ → κΛorWA → Ωe2πΓK → ξΔNΤd6 → θvPΡlC → Υr9ιpO → Ωv1ρlK → πΔ9ιd4 → μΩPΡJ8 → δΕqpcG → ΜS0ςΟW → ςmeΒu2 → πN7λΥ4 → μδvkF8 → δΝAθUG → ΧΜhyVM → zgGβΑi → ΚKGβΨY → ΚΓaΖeY → bVNΤΜΗ → vgUΜΑm → hK8κΨΑ → βΓIΩeI → ΘΖNΤba → vXTΝΚm → jc8κΕy → βSEδΟI → ΞΘluZU → jY8κΙy → βaEδΗI → ΞΘVΛZU → jfXΙΒy → bMEδΦΗ → ΞyUΜiU → jhFγzy → ΜIEδαW → ΞΗeΒaU → jWMΥΛy → xeEδΓk → ΞOCζΤU → ΣuixmQ → rF7λδq → δΝ0ςUG → ςΜhyV2 → πgGβΑ4 → μΚJΨX8 → δΔbΕdG → ΜTPΡΞW → rkeΒwq → NC0ςηΦ → ςΤwjO2 → πuCζm4 → μΣ7λP8 → εγroGF → ΞΛ2πWU → ξjdΓx6 → θPDεΣC → ΥΠroRO → vo2πsm → ξ93οκ6 → μθΩIB8 → δΦΕbMG → ΜySΞiW → lfFγΒw → ΜMAθΦW → ΧyeΒiM → zNFγΥi → ΜwGβkW → ΚfBηΒY → ΥbLΦΖO → zvTΝli → jH9ιβy → ΩΙEδYK → ΞΔZΗdU → jXPΡΚy → rcEδΕq → ΞS0ςΟU → ςmixu2 → πF7λδ4 → μδΜUF8 → δΝgzUG → ΜiIΩyW → ΖfFγΒc → ΜTLΦΞW → zkeΒwi → NHBηβΦ → ΥΙwjYO → vaCζΗm → ΣW8κΛQ → βrdΓpI → ΘP1ρΣa → πsWΚo4 → μd3οΔ8 → μδPΡF8 → δΝqpUG → Μi0ςyW → ςfFγΒ2 → πΜLΦV4 → μzfΑh8 → δLHαΧG → ΜΘzgZW → fYIΩΙΓ → ΖaMΥΗc → xWSΞΛk → leCζΓw → ΣOAθΤQ → ΧuqpmM → z80ςλi → ςγGβG2 → πΛΙXW4 → μeaΖΓ8 → δVNΤΜG → ΜvfΑlW → fL9ιΧΓ