Base 103: 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
25 max steps10 → 0ρ → π1 → ξ3 → κ7 → βF
352 max steps100 → 0ρρ → πρ1 → ορ2 → ξρ3 → νρ4 → μρ5 → λρ6 → κρ7 → ιρ8 → θρ9 → ηρA → ζρB → ερC → δρD → γρE → βρF → αρG → ΩρH → ΨρI → ΧρJ → ΦρK → ΥρL → ΤρM → ΣρN → ΡρO → ΠρP → ΟρQ → ΞρR → ΝρS → ΜρT → ΛρU → ΚρV → ΙρW → ΘρX → ΗρY → ΖρZ → Ερa → Δρb → Γρc → Βρd → Αρe → zρf → yρg → xρh → wρi → vρj → uρk → tρl → sρm → rρn → qρo → pρp
44 max stepsq000 → pρρp → popq → 1ρρπ → π0π2
540 max steps30000 → 2ρρρο → ο1ρο3 → πλρ52 → οκρ63 → ξθρ84 → νερB5 → μαρF6 → λΥρK7 → κΞρQ8 → ιΗρX9 → θyρfA → ηpρoB → ζfρyC → εnρqD → δeρzE → γmρrF → βdρΑG → αlρsH → ΩcρΒI → ΨkρtJ → ΧbρΓK → ΦjρuL → ΥaρΔM → ΤiρvN → ΣZρΕO → ΡhρwP → ΠYρΖQ → ΟgρxR → ΞXρΗS → ΝfρyT → ΜWρΘU → ΛeρzV → ΚVρΙW → ΚcρΒW → ΙWρΘX → ΙaρΔX → ΘXρΗY → ΘYρΖY → ΗYρΖZ → ΗWρΘZ
6254 max stepsm000zz → zzlsfg → KJ6κΧΧ → δΓΑdcE → ΞQMΣΟS → voktqk → B91οθη → ξΨΤLI4 → κΕwha8 → βUEβΛG → ΜΚfyVU → heIΧΑy → ΔMGΩΤc → ΘwQΞiY → nZDγΖs → ΞW4μΙS → θlbΓtA → ΧR7ιΞK → βΒlsdG → ΚO6κΡW → δscΒmE → ΞP5λΠS → ζqktoC → Σ91οθO → ξΨslI4 → κΕ6κa8 → δβTΛFE → ΞΛgxUS → lgGΩyu → ΘI8θΨY → ΩΕYΖaI → ΖXTΛΘa → haUΚΕy → fUGΩΛΑ → ΘgKΥyY → zZHΨΖg → ΖWIΧΙa → ΔcUΚΓc → fRPΟΞΑ → pmKΥsq → z60πλg → πεIΧC2 → ξΡΓbO4 → κsQΞm8 → βn5λrG → ζΚ3νVC → κΣdΑN8 → βuMΣkG → Κv9ηjW → ΧdBεΒK → ΣΒNΡdO → usNΡml → t95λθm → ζΨ6κIC → δΣΔaNE → ΞuSΜkS → lj9ηvu → ΧC8θεK → ΩΡΑdOI → ΖsMΣma → vV5λΚk → ζeAζΑC → ΥΣLΤNM → ywtkih → HE8θγα → ΩΝΗXSI → ΖkYΖua → XV9ηΚΙ → ΧeaΔΑK → ΒTLΤΜe → xiMΣwi → vFDγβk → ΞΛAζUS → ΥlfytM → xJ7ιΧi → βΓEβcG → ΜΚPΟVU → phdΑxq → NG0παΤ → πΙujW2 → ξcAζΓ4 → κΥPΟL8 → βyopgG → ΚI0πΨW → πΕcΒa2 → ξUOΠΛ4 → κrfyn8 → βJ3νΧG → κΚΒcV8 → βeOΠΑG → ΚrLΤnW → xd3νΒi → κOEβΡ8 → βΜrmTG → Κi4μwW → θdDγΒA → ΧΞNΡRK → Βtlsle → N86κιΤ → δαujGE → ΞΙAζWS → ΥlbΓtM → xR7ιΞi → βmEβsG → ΜΚ5λVU → ζhdΑxC → ΣNFαΣO → ΚuslkW → dA6κηΓ → δΦOΠKE → ΞΑqneS → lM2ξΤu → μw8θi6 → ζΩDγHC → ΣΞΖYRO → tmWΘsm → b75λκΕ → ζγSΜEC → ΣΝivSO → tkCδum → ΠA6κηQ → δΦopKE → ΞΑ0πeS → πlLΤt2 → ξx7ιh4 → κβFαF8 → βΛΙVUG → ΚgcΒyW → dPHΨΠΓ → ΖqOΠoa → rV1οΚo → ξe2ξΑ4 → μκLΤ76 → ζγwhEC → ΣΝEβSO → ΜtjulU → hB7ιζy → βΤGΩMG → ΚΘviXW → daCδΕΓ → ΠUOΠΛQ → rpfypo → J2ρρξΨ → οΧEβJ3 → μΜΒcT6 → ζiOΠwC → ΣrDγnO → Ξt3νlS → κl7ιt8 → γα7ιGF → βΜΘWTG → ΚiaΔwW → dTDγΜΓ → ΞiOΠwS → rlDγto → Ξ82ξιS → μαktG6 → ζΙ8θWC → ΩΣbΓNI → ΖuQΞka → nV9ηΚs → Χe4μΑK → θΒLΤdA → ΧxNΡhK → ΒtFαle → ΚN7ιΣW → βucΒkG → ΚP9ηΠW → ΧqcΒoK → ΒP1οΠe → ξqMΣo4 → κv1οj8 → ξβBεF4 → κΣΚUN8 → βuezkG → ΚL9ηΥW → ΧycΒgK → ΒPHΨΠe → ΖqMΣoa → vV1οΚk → ξeAζΑ4 → κΥLΤL8 → βywhgG → ΚIEβΨW → ΜΕcΒaU → hUOΠΛy → rgGΩyo → ΘI2ξΨY → μΕYΖa6 → ζXTΛΘC → ΣhZΕxO → tVFαΚm → Κe6κΑW → δdLΤΒE → ΞxNΡhS → tlFαtm → Κ86κιW → δαcΒGE → ΞΙOΠWS → rlbΓto → R82ξιΟ → μαmrG6 → ζΙ4μWC → θΣbΓNA → ΧuQΞkK → Βn9ηre → ΧN3νΣK → κΒtkd8 → βO8θΡG → ΩΚrmVI → Ζe4μΑa → θVLΤΚA → ΧxdΑhK → ΒNFαΣe → ΚuMΣkW → vd9ηΒk → ΧOAζΡK → ΥΒrmdM → xO4μΡi → θsEβmA → ΧΜ5λTK → ζΒhwdC → ΣOEβΡO → ΜtrmlU → h84μιy → θαGΩGA → ΧΙΗXWK → ΒcYΖΓe → XQMΣΟΙ → voaΔqk → TB1οζΝ → ξΤivM4 → κwCδi8 → βΠDγPG → ΞΚpoVS → le0πΑu → πM8θΤ2 → ξΩviH4 → κΗCδY8 → βΠXΗPG → ΚqYΖoW → dX1οΘΓ → ξaOΠΕ4 → κrTΛn8 → βh3νxG → κΚFαV8 → βΚdΑVG → ΚeMΣΑW → vdLΤΒk → xOAζΡi → ΥsEβmM → Μx5λhU → ζhFαxC → ΣΚFαVO → ΚtdΑlW