Base 109: 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 → 0χ → φ1 → τ3
355 max steps100 → 0χχ → φχ1 → υχ2 → τχ3 → σχ4 → ςχ5 → ρχ6 → πχ7 → οχ8 → ξχ9 → νχA → μχB → λχC → κχD → ιχE → θχF → ηχG → ζχH → εχI → δχJ → γχK → βχL → αχM → ΩχN → ΨχO → ΧχP → ΦχQ → ΥχR → ΤχS → ΣχT → ΡχU → ΠχV → ΟχW → ΞχX → ΝχY → ΜχZ → Λχa → Κχb → Ιχc → Θχd → Ηχe → Ζχf → Εχg → Δχh → Γχi → Βχj → Αχk → zχl → yχm → xχn → wχo → vχp → uχq → tχr → sχs
44 max stepst000 → sχχs → srst → 1χχφ → φ0φ2
542 max steps10006 → 60χφς → χοχ71 → φοχ72 → υξχ83 → τμχA4 → σιχD5 → ςεχH6 → ρΩχM7 → πΣχS8 → οΛχZ9 → ξΓχhA → νtχqB → μjχΑC → λpχuD → κiχΒE → ιoχvF → θhχΓG → ηnχwH → ζgχΔI → εmχxJ → δfχΕK → γlχyL → βeχΖM → αkχzN → ΩdχΗO → ΨjχΑP → ΧcχΘQ → ΦiχΒR → ΥbχΙS → ΤhχΓT → ΣaχΚU → ΡgχΔV → ΠZχΛW → ΟfχΕX → ΞYχΜY → ΝeχΖZ → ΜXχΝa → ΞbχΙY → ΝbχΙZ → ΜaχΚa → ΛaχΚb → ΛYχΜb
6250 max stepso000zz → zznwlm → ED8ξκκ → ζΦΤRQI → Μuqtqa → b42τσΛ → ςοYΜ86 → μηcΘGC → ΩΟUΠWO → zlhΓzm → LECκιγ → ΧΤΕfSQ → vqOΧuq → x53σςo → πν8ξA8 → θζβKHG → ΠΝΕfYW → jeOΧΗΓ → xSIδΤo → Κq8ξuc → ζX3σΞI → πΜfΕZ8 → θcOΧΙG → ΠxVΟnW → ki9νΓΒ → δKGζγK → ΞΘΖedY → fUQΥΡΗ → tmQΥys → tC0φλs → φΨ0φO2 → φτxm32 → τρAμ64 → πλαLC8 → θΨΓhOG → ΠyKβmW → ΖjBλΒg → ΩPHεΧO → Μzvola → bE6πιΛ → κΤYΜSE → ΥqcΘuS → rV3σΠu → πk2τΑ8 → ςθFηF6 → μΡΟVUC → ΩmiΒyO → zJBλδm → ΩΙCκcO → ΧzVΟlQ → vjDιΒq → ΥI4ςεS → ξΛqtaA → δa2τΛK → ςΘZΛd6 → μbTΡΚC → ΩnXΝxO → zf9νΖm → δQCκΦK → ΧΘtqdQ → vU2τΡq → ςm4ςy6 → ξμBλBA → δαΨNMK → ΘΓylie → TKCκγΤ → ΧΗoveQ → vS6πΤq → κq4ςuE → ξΥ3σRA → πδrsJ8 → θΙ0φcG → φΠVΟV2 → τkiΒΑ4 → πJFηδ8 → θΠΘcVG → ΠkUΠΑW → ljFηΒΑ → ΠIEθεW → ΣΛiΒaU → naIδΛy → ΚaAμΛc → βaWΞΛM → ΔhZΛΔi → bMKβαΛ → ΖΓYΜig → dPJγΧΙ → ΘwUΠoe → lT7οΣΑ → θoEθwG → ΣΠ7οVU → θnjΑxG → ΠH9νζW → δΝiΒYK → ΘeIδΗe → ΚTRΤΣc → roWΞwu → h82τοΕ → ςηMΩG6 → μΟΑjWC → ΩiGζΓO → ΞzJγlY → ΘfDιΖe → ΥTPΦΣS → vrnwtq → 951υςο → τνεHA4 → πγΛZK8 → θΗaΚeG → ΠZRΤΜW → rjbΙΒu → XI2τεΟ → ςΛgΔa6 → μaMΩΛC → ΩΒZΛjO → zbHεΚm → ΜYCκΝa → ΧeaΚΗQ → vZRΤΜq → rc4ςΙu → ξW2τΟA → ςδhΓJ6 → μΙKβcC → ΩΖVΟfO → zjPΦΒm → vICκεq → ΧΛ4ςaQ → ξvZΛpA → δb5ρΚK → μΘXΝdC → ΩfTΡΖO → znPΦxm → vD9νκq → δΦ4ςQK → ξΘtqdA → δU2τΡK → ςΘlyd6 → μUCκΡC → ΩΧlyPO → zwCκom → ΧD7οκQ → θΦupQG → Πu4ςqW → ξj3σΒA → πδHεJ8 → θΜΘcZG → ΠcUΠΙW → ljVΟΒΑ → jIEθεΓ → ΣΛIδaU → ΚnZΛxc → bX9νΞΛ → δgYΜΕK → ΘdNΨΘe → zUSΣΡm → pmCκyw → ΧC6πλQ → κΨupOE → Υy4ςmS → ξrBλtA → δΩ1υNK → τΘzkd4 → πUEθΡ8 → θΣlyTG → ΠoCκwW → Χj7οΒQ → θvHεpG → ΠΜ5ρZW → μjbΙΒC → ΩXHεΞO → ΜzfΕla → bPDιΧΛ → ΥwYΜoS → rd7οΘu → θU2τΡG → ςΠlyV6 → μkCκΑC → ΩΧFηPO → ΠzvolW → jE6πιΓ → κΤIδSE → ΥΚpubS → rY4ςΝu → ξe2τΗA → ςδRΤJ6 → μΙqtcC → ΩW2τΟO → ςzhΓl6 → μLDιβC → ΩΥΔgRO → zsMΩsm → ΒCχχκk → λΑVΟkD → ΧjFηΒQ → ΠvHεpW → Μj5ρΒa → μbHεΚC → ΩΜXΝZO → zfbΙΖm → XQCκΦΟ → ΧugΔqQ → vN3σΩq → πΑ4ςk8 → ξθFηFA → δΡΟVUK → ΘmiΒye → TJBλδΤ → ΩΙovcO → zW6πΟm → κiCκΓE → ΧΥJγRQ → Θvrspe → T60φρΤ → φλovC2 → τΨ6πO4 → πκxmD8 → θΦAμQG → βΠtqVM → Δk2τΑi → ςLFηβ6 → μΠΔgVC → ΩkMΩΑO → ΒzFηlk → ΠHDιζW → ΥΝiΒYS → reIδΗu → ΚS2τΤc → ςqWΞu6 → μh3σΔC → πΩLαN8 → θΔzkhG → ΠMEθαW → ΣΓiΒiU → nKIδγy → ΚΗAμec → βXRΤΞM → ΔrfΕti → PL1υβΨ → τΕwng4 → πO8ξΨ8 → θζxmHG → ΠΝAμYW → βjdΗΒM → ΔTHεΣi → ΜoKβwa → Ζb7οΚg → θYOΧΝG → ΠxdΗnW → jT9νΣΓ → δoIδwK → ΚΘ7οdc