Base 116: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР

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
214 max steps20 → 1Г → Б3χ7οFΨVιLΛhwvГ1Б3
360 max steps100 → 0ДД → ГД1 → ВД2 → БД3 → АД4 → ωД5 → ψД6 → χД7 → φД8 → υД9 → τДA → σДB → ςДC → ρДD → πДE → οДF → ξДG → νДH → μДI → λДJ → κДK → ιДL → θДM → ηДN → ζДO → εДP → δДQ → γДR → βДS → αДT → ΩДU → ΨДV → ΧДW → ΦДX → ΥДY → ΤДZ → ΣДa → ΡДb → ΠДc → ΟДd → ΞДe → ΝДf → ΜДg → ΛДh → ΚДi → ΙДj → ΘДk → ΗДl → ΖДm → ΕДn → ΔДo → ΓДp → ΒДq → ΑДr → zДs → yДt → xДu → wДv → vДwvДw
424 max steps700T → T6χβ → ρvvE → βДДS → βRβT → yvvu → 3ДДБ → Б2Б4 → ωφ76 → σξFC → ηΧVOΗpΒmKBςληΞdOΗZΣmiJκΛΟRβeyZΣui3АΛχRβ8οxtGΨ3АWχpΒ8οBςGηΧVO
549 max stepsv0000 → uДДДx → xtДxv → y1ДВu → ГuДw2 → ВvДv3 → БtДx4 → АuДw5 → ωsДy6 → ψtДx7 → χrДz8 → φsДy9 → υqДΑA → τrДzB → σpДΒC → ςqДΑD → ρoДΓE → πpДΒF → οnДΔG → ξoДΓH → νmДΕI → μnДΔJ → λlДΖK → κmДΕL → ιkДΗM → θlДΖN → ηjДΘO → ζkДΗP → εiДΙQ → δjДΘR → γhДΚS → βiДΙT → αgДΛU → ΩhДΚV → ΨfДΜW → ΧgДΛX → ΦeДΝY → ΥfДΜZ → ΤdДΞa → ΣeДΝb → ΡcДΟc → ΠdДΞd → ΟbДΠe → ΡaДΡc → ΣdДΞb → ΡdДΞcΠcДΟdΠbДΠdΡbДΠcΡdДΞc
6654 max stepsT000dh → hdSαΟΜ → wbTΩΡw → ueДДΝy → ΞxDπuf → γY2БΥS → ωykΗt6 → σM4ωθC → υηΙiNA → λΘPδkK → ΟΓMηpe → ΙaCρΣk → εhNζΛQ → ΗΓSαpm → wKCρκw → εΝДДeQ → δΞFξeR → ΨΑYΤrW → qk8υΘΓ → νNBςηI → ηΤΗkZO → ΗjLθΙm → ΛPJκεi → ΟΔRβoe → yaEοΣu → αh3АΛU → χuSαx8 → οw2БvG → ωΨ0ГV6 → ГσqΑB2 → Бθ9τM4 → χλΙiJ8 → οΠPδcG → ΨΓcΟpW → qcCρΠΓ → εdBςΟQ → ηΓaΡpO → ΗgCρΜm → εVJκΨQ → ΟΓqΑpe → aD9τρΤ → λδhΚQK → ΟΒRβqe → yaAσΣu → ιh3АΛM → χΛSαh8 → οwSαvG → Ψw0ГvW → Гq0ГΒ2 → ГБAσ32 → БψθL64 → χςΚhC8 → οζRβOG → ΨΖxtmW → qJ3АλΓ → χΠBςc8 → οηcΟNG → ΨΘbΠkW → qeMηΞΓ → ΙZBςΤk → ηjNζΙO → ΘΖOεml → ΕMIλθo → ΡΚFξic → ΨeQγΞW → ΑqYΤΒs → kB7φσΙ → οθNζMG → ΨΚΖliW → qRJκγΓ → ΟzBςse → ηa6χΣO → ρΗgΛlE → γUKιΩS → Νysytg → W64ωψΨ → υςpΒCA → λζBςOK → ηΟΕmdO → ΗbHμΡm → ΤfJκΝa → ΟiWΦΚe → oaQγΣΕ → ΑhFξΛs → ΨT7φαW → οvpΒwG → ΨC0ГςW → ГζpΒO2 → БΖBςm4 → χηIλN8 → οΡΗkbG → ΨfLθΝW → ΛqWΦΒi → oSAσβΕ → ιxFξuM → ΨΛ2БhW → ωqSαΒ6 → σwAσvC → ιη0ГNM → ГΛΗkh2 → БTLθα4 → χΛuwh8 → οT1ВαG → БΨuwV4 → χr1ВΑ8 → Бο8υF4 → χνΨUH8 → οΥrzYG → Ψl7φΗW → οqKιΒG → ΨΝAσfW → ιqWΦΒM → ΛoAσΔi → ιSEοβM → αΛwuhU → uT1Вαy → Бv3Аw4 → ψφ0Г87 → ГρνGD2 → БδΥXQ4 → χΒlΖq8 → οKAσκG → ιΨΝeVM → ΛrXΥΑi → mS8υβΗ → νxJκuI → ΤΟ2Бda → ωiaΡΚ6 → σgQγΜC → ηΑUΨrO → Ηs8υzm → νK6χκI → ρΤΝeZE → γjXΥΙS → ymOεΖu → ΕJ3Аλo → χΠFξc8 → οΨcΟVG → ΨrbΠΑW → qe8υΞΓ → νZBςΤI → ηΤiΙZO → ΗjPδΙm → ΓPJκεq → ΟΔBςoe → ηaEοΣO → αΗgΛlU → uUKιΩy → Νt3Аyg → χW4ωΧ8 → υοoΓFA → λΩDπUK → γΟsydS → yb5ψΡu → σf3АΝC → χηWΦN8 → οΘnΔkG → ΨNFξηW → ΨΘpΒkW → qNBςηΓ → ηΘBςkO → ηΗMηlO → ΙΗKιlk → ΝOKιζg → ΝΖVΧmg → qWIλΧΓ → ΡpBςΓc → ηeCρΞO → εΗYΤlQ → ΓkKιΘq → ΝNBςηg → ηΘVΧkO → ΗqMηΒm → ΙKAσκk → ιΞNζeM → ΛΗYΤli → kSKιβΙ → ΝxNζug → ΗW2БΧm → ωpJκΓ6 → σΟCρdC → ηεaΡPO → ΗΔfΜom → WKEοκΨ → αΞpΒeU → uZBςΤy → ηj3АΙO → χΗOεl8 → οΕKιnG → ΨΝGνfW → ΦqWΦΒY → omAσΖΕ → ιJFξλM → ΨΠΚhcW → qdRβΟΓ → ybBςΡu → ηf3АΝO → χΗWΦl8 → οoKιΔG → ΨΝEοfW → αqWΦΒU → uoAσΔy → ιF3АοM → χΩΚhU8 → οtRβyG → Ψy4ωtW → υq4ωΒA → υλAσJA → λιΟcLK → ΟΜbΠge → eaUΨΣΟ → shZΣΛΑ → iT7φαΛ → οvRβwG → Ψy0ГtW → Гq4ωΒ2 → БυAσ94 → χμθLI8 → οΣΚhaG → ΨhRβΛW → yqSαΒu → wB3Аσw → χηДДM8 → φθFξM9 → νΨΙiVI → ΤrPδΑa → Γi8υΚq → νRBςγI → ηΤysZO → Ηj5ψΙm → σPJκεC → ηΟΓodO → ΗbDπΡm → γfJκΝS → ΟyWΦte → oa4ωΣΕ → υhFξΛA → λΨSαVK → ΟwqΑve → aA0ГτΤ → ГκhΚK2 → БΞRβe4 → χyYΤt8 → οk4ωΘG → υΨMηVA → λΙqΑjK → ΟP9τεe → λΔZΣoK → ΟiEοΚe → αaQγΣU → ΑugΛxs → U82Бφα → ωξtxG6 → σΧ3АWC → χηoΓN8 → οΘDπkG → γΨMηVS → ΙyqΑtk → OA4ωτη → υκΖlKA → λΞJκeK → ΠΞYΤed → kcYΤΠΙ → kdNζΟΙ → ΗbNζΡm → ΗfJκΝm → ΟXJκΦe → ΟnZΣΕe → iaGνΣΛ → ΦhRβΛY → ymSαΖu → wJ3Аλw → χΟДДc8 → φΠVΧc9 → νqcΟΒI → ΤcAσΠa → ιicΟΚM → ΛcQγΠi → ΑdRβΟs → yb7φΡu → οf3АΝG → χΨWΦV8 → οrnΔΑG → ΨG8υξW → νΧpΒWI → ΤpBςΓa → ηiCρΚO → εΗQγlQ → ΓΑKιrq → ΝC8υςg → νζVΧOI → ΤΖpΒma → iJBςλΛ → ηΠRβcO → ΗycΟtm → cK4ωκΡ → υΞdΞeA → λaYΤΣK → ΟkgΛΘe → aUMηΩΤ → ΙthΚyk → SO4ωζγ → υΖxtmA → λJ3АλK → χΠΞdc8 → οdZΣΟG → ΨiaΡΚW → qgQγΜΓ → ΑVBςΨs → ηr7φΑO → οΗ8υlG → νΨKιVI → ΤΝqΑfa → iX9τΦΛ → λnRβΕK → ΟyGνte → Φa4ωΣY → υmgΛΖA → λUIλΩK → ΡΟsydc → eb5ψΡΟ → σfZΣΝC → ηiWΦΚO → ΗoQγΔm → ΑKEοκs → αΞ7φeU → οuYΤxG → Ψk2БΘW → ωqMηΒ6 → σΙAσjC → ιηOεNM → ΛΘΔnki → SNFξηγ → ΨΘxtkW → qN3АηΓ → χΘBςk8 → οηMηNG → ΨΙΗkjW → qPLθεΓ → ΛΔBςoi → ηSEοβO → αΗwulU → uL1Вιy → БΜ3Аg4 → ψφUΨ87 → ρξrzGE → γΧ7φWS → οyoΓtG → ΨE4ωπW → υβpΒSA → λxBςuK → ηΟ2БdO → ωΗaΡl6 → σgKιΜC → ηΝUΨfO → ΗsWΦzm → oK6χκΕ → ρΞFξeE → γΨYΤVS → yrjΘΑu → O93Аυη → χμΖlI8 → οΣJκaG → ΨΟgΛdW → qbTΩΡΓ → ufBςΝy → ηX3АΦO → χΗmΕl8 → οLHμιG → ΨΤΛgZW → qjTΩΙΓ → uPBςεy → ηΔ3АoO → χΗEοl8 → οαKιTG → ΨΝuwfW → qX1ВΦΓ → БnBςΕ4 → χηGνN8 → οΦΗkXG → ΨnLθΕW → ΛqGνΒi → ΦSAσβY → ιxlΖuM → ΛK2Бκi → ωΞRβe6 → σyYΤtC → ηk4ωΘO → υΗMηlA → λΙKιjK → ΟΝOεfe → ΕaWΦΣo → ohFξΛΕ → ΨTFξαW → ΨvpΒwW → qC0ГςΓ → ГζBςO2 → БηΕmN4 → χΘHμk8 → οΤMηZG → ΨΙiΙjW → qQOεδΓ → ΕΒBςqo → ηGAσξO → ιΧΖlWM → ΛpJκΓi → ΟSCρβe → εxZΣuQ → Γi2БΚq → ωRBςγ6 → σηysNC → ηΘ5ψkO → σΗMηlC → ηΙKιjO → ΝΗOεlg → ΕWKιΧo → ΝpFξΓg → ΨWCρΧW → εqoΓΒQ → ΓEAσπq → ιβBςSM → ηΛwuhO → ΗT1Вαm → БvJκw4 → χΟ0Гd8 → ГοaΡF2 → БΩfΜU4 → χtVΧy8 → οq4ωΒG → υΨAσVA → λιqΑLK → ΟΜ9τge → λaUΨΣK → ΟsgΛze → aU6χΩΤ → ρthΚyE → γS4ωβS → υywutA → λ51ВωK → БτΞdA4 → χκZΣK8 → οΞhΚeG → ΨZRβΤW → yqiΙΒu → QB3Аσε → χθΒpM8 → οΚBςiG → ηΨQγVO → ΗΑqΑrm → KA8υτλ → νκΞdKI → ΤΞZΣea → jhYΤΛΚ → kTPδαΙ → ΓvNζwq → ΗC0Гςm → ГζJκO2 → БΟΕmd4 → χbHμΡ8 → οΤeΝZG → ΨjXΥΙW → qmOεΖΓ → ΕJBςλo → ηΠFξcO → ΨΗcΟlW → qcKιΠΓ → ΝdBςΟg → ηbVΧΡO → ΗqeΝΒm → YKAσκΦ → ιΞlΖeM → ΛZJκΤi → ΟjRβΙe → yaOεΣu → Εh3АΛo → χTFξα8 → οΨuwVG → Ψr1ВΑW → Бq8υΒ4 → χνAσH8 → οιΤYLG → ΨΜjΘgW → qVNζΨΓ → ΗrBςΑm → ηK8υκO → νΞΖleI → ΤZJκΤa → ΟjhΚΙe → aSOεβΤ → ΕxhΚuo → SG2Бξγ → ωΧxtW6 → σp3АΓC → χηCρN8 → οεΗkPG → ΨΔLθoW → ΛqEοΒi → αSAσβU → ιxtxuM → Λ42БАi → ωφRβ86 → σξxtGC → ηΧ3АWO → χΗoΓl8 → οLDπιG → γΨΛgVS → yrTΩΑu → u93Аυy → χμ3АI8 → χοΡaF8 → οΩfΜUG → ΨtVΧyW → rp4ωΓΒ → υD9τρA → μκγQKJ → ΡΞzrec → eZ7φΤΟ → οjZΣΙG → ΨiOεΚW → ΕqQγΒo → ΑGAσξs → ιΧ7φWM → οΛoΓhG → ΨTDπαW → γvpΒwS → yC0Гςu → Гζ3АO2 → БχΕm74 → χπHμE8 → οβΣZSG → ΨxhΚuW → qS2БβΓ → ωxBςu6 → ση2БNC → ωηΗkN6 → σΘLθkC → ηΛMηhO → ΙΗSαlk → wOKιζw → ΝΕДДmg → ΜΖ7φmh → οUIλΩG → ΨΡsybW → qf5ψΝΓ → σXBςΦC → θζmΕON → 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