Base 121: 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
233 max steps10 → 0Й → И1 → Ж3В7τFδVψBμNΜlΘpΩZΠhθRΔtπJΥdzxЖ3
363 max steps100 → 0ЙЙ → ИЙ1 → ЗЙ2 → ЖЙ3 → ЕЙ4 → ДЙ5 → ГЙ6 → ВЙ7 → БЙ8 → АЙ9 → ωЙA → ψЙB → χЙC → φЙD → υЙE → τЙF → σЙG → ςЙH → ρЙI → πЙJ → οЙK → ξЙL → νЙM → μЙN → λЙO → κЙP → ιЙQ → θЙR → ηЙS → ζЙT → εЙU → δЙV → γЙW → βЙX → αЙY → ΩЙZ → ΨЙa → ΧЙb → ΦЙc → ΥЙd → ΤЙe → ΣЙf → ΡЙg → ΠЙh → ΟЙi → ΞЙj → ΝЙk → ΜЙl → ΛЙm → ΚЙn → ΙЙo → ΘЙp → ΗЙq → ΖЙr → ΕЙs → ΔЙt → ΓЙu → ΒЙv → ΑЙw → zЙx → yЙyxЙzyЙy
459 max stepsz000 → yЙЙy → yxyz → 1ЙЙИ → И0И2ИЕ32ЖБ74ВσF8τγVGδuΒWv6ВΓφ6ВEφηREθΓtSΔ8Аuς8АIςΨZIΩmΚanMμΛΞMμkΞSζkΒSζwΒ4ДwА4ДAАοJAπΤdKΥeΣefcΥΤhcΥΡhYΩΡpYΩΙpIπΙΧIπcΧiΞcjUδΟxUδΑx2ЖΑД2Ж6ДχB6ψλNCμΛlOΜOκmΚOκoΚKξoΣKξgΣaΧglaΧΝlQθΝΖQθsΖCφsκCφQκΗpQΘGςqβGςYβqΖYrEτΗζEτUζyxUz0ИyИ0И2
550 max steps30000 → 2ЙЙЙЗ → З1ЙЗ3 → ИГЙ52 → ЗВЙ63 → ЖАЙ84 → ЕχЙB5 → ДσЙF6 → ГξЙK7 → ВθЙQ8 → БαЙX9 → АΡЙfA → ωΘЙoB → ψxЙyC → χnЙΙD → φwЙzE → υmЙΚF → τvЙΑG → σlЙΛH → ςuЙΒI → ρkЙΜJ → πtЙΓK → οjЙΝL → ξsЙΔM → νiЙΞN → μrЙΕO → λhЙΟP → κqЙΖQ → ιgЙΠR → θpЙΗS → ηfЙΡT → ζoЙΘU → εeЙΣV → δnЙΙW → γdЙΤX → βmЙΚY → αcЙΥZ → ΩlЙΛa → ΨbЙΦb → ΧkЙΜc → ΦaЙΧd → ΨhЙΟb → ΧeЙΣc → ΦgЙΠd → ΥdЙΤe → ΥeЙΣe → ΤeЙΣf → ΤcЙΥfΦdЙΤdΥgЙΠeΤcЙΥf
6713 max stepsZ000vx → xvYΩΒΑ → p62ЖГΙ → ДχIπC6 → ψλΦbOC → μΛiΞmO → ΜVNλδm → ΜwOκΑm → ΚP3Еκo → ВΙKξo8 → τΣJοfG → δΥbΦdW → vjfΡΞΓ → bU6ВεΨ → φykΜyE → θQЙЙθS → ιζЙЙSR → θη2ЖSS → ДΔΒut6 → ψA6ВωC → φολNKE → θΤΛleS → ΔeOκΤu → Κe8АΤo → ςeKξΤI → ΩΣdΤfa → nfbΦΣΛ → jcMμΦΟ → ΞiUδΟk → xWSζγΑ → Βu2ЖΓw → Д84ДБ6 → АψςGBA → πναXMK → ΥΟqΖie → fWEτγΤ → ζucΥΓU → zh7БΠy → τY0ИαG → ИδpΗV2 → ЖwGςΑ4 → Вβ3ЕX8 → ВτrΕF8 → τεCφUG → κδxyVQ → Θw0ИΑq → ИH3Еς2 → ЖВΩY74 → ВυoΘE8 → τηIπSG → δΧΒubW → vk6ВΝΓ → φS6ВηE → φθΒuRE → θΕ6ВsS → φΔBχtE → μθ9ωRO → πΜΔslK → ΥQAψιe → ξΗeΣqM → ΠdFσΥi → δgWβΡW → vtZΨΔΓ → nA6ВωΛ → φοMμKE → θΤΝjeS → ΔeSζΤu → Βe8АΤw → ςe4ДΤI → АΩdΤZA → πoeΣΙK → ΥdJοΥe → ΥgeΣΡe → fdZΨΥΤ → ngcΥΡΛ → haMμΨΡ → ΞmYΩΛk → pTNλζΙ → ΜΑIπwm → ΧP3Еκc → ВΙiΞo8 → τVJοδG → δΥvΑdW → vg4ДΡΓ → Аa6ВΨA → φπlΛJE → θΦOκcS → ΚΔhΟto → XL9ωξγ → πΡsΔgK → ΥaAψΨe → ξmeΣΛM → ΠdNλΥi → ΜgWβΡm → taOκΨΕ → ΚmAψΛo → ξOKξλM → ΣΠΚmhg → bYMμαΨ → ΞqkΜΗk → TRFσθη → δΕΑvsW → vC4ДχΓ → Аλ6ВOA → φπΚmJE → θΦMμcS → ΞΔhΟtk → XT9ωζγ → πΑsΔwK → ΥB3Еψe → ВνeΣM8 → τΟcΥiG → δhVγΠW → wuXαΓΒ → r84ДБΗ → АσEτGA → πζβWTK → ΥΑsΔwe → fB3ЕψΤ → ВνcΥM8 → τΟgΠiG → δZVγΩW → wunΙΓΒ → L84ДБο → АσΡfGA → πγaΧWK → ΥukΜΓe → fR7БθΤ → τΕcΥsG → δhBχΠW → μvXαΒO → Μr5ГΖm → ψPDυκC → μθΘoRO → ΜΕIπsm → ΧPBχκc → μΙiΞoO → ΜVJοδm → ΥwOκΑe → Κf3ЕΣo → ВcKξΦ8 → τΣhΟfG → δcWβΦW → vthΟΔΓ → XA6Вωγ → φοsΔKE → θΤAψeS → ξΔdΤtM → Πf9ωΣi → πcWβΦK → ΥthΟΔe → fX9ωβΤ → πscΥΕK → ΥhBχΠe → μfXαΣO → ΜrbΦΖm → jPDυκΟ → θΙUδoS → ΔxJοzu → Υ91ЗАe → ЖρeΣI4 → ВΨcΥa8 → τmgΠΛG → δZNλΩW → ΜvnΙΒm → PL5Гξλ → ψΡΙngC → μaKξΨO → ΣΜlΛlg → bQOκιΨ → ΚΗkΜqo → RLFσξι → δΡΕrgW → vaCφΨΓ → κm6ВΛQ → φΘNλpE → θΜHρlS → ΩΔPιta → Θn9ωΚq → πMGςνK → βΥΞidY → rgUδΡΗ → xaEτΨΑ → ζm2ЖΛU → ДzNλx6 → ψΜ1ЗlC → ЖμPιN4 → ВΝΗpk8 → τSGςηG → δβΒuXW → vs6ВΕΓ → φC6ВχE → φληROE → θΛΓtmS → ΔO8Аλu → ςΛ8АmI → ςΩNλZI → ΩΜnΙla → nQKξιΛ → ΣΗMμqg → ΞbFσΧk → δkSζΝW → ΒvRηΒw → Δ64ДГu → Аχ8АCA → ςπκOJI → ΩΦΙnca → niKξΟΛ → ΣWMμγg → ΞuaΧΓk → lT7БζΝ → τΑQθwG → δΖ3ЕrW → ВvDυΒ8 → τθ5ГRG → ψδΔsVC → μwAψΑO → ξΜ3ЕlM → ВΠPιh8 → τΘXαpG → δrHρΖW → ΩvDυΒa → θn5ГΚS → ψΔLνtC → μΠ9ωhO → πΜXαlK → ΥrPιΖe → ΘfDυΣq → θcGςΦS → βΔhΟtY → rX9ωβΗ → πsEτΕK → ζΥBχdU → μzfΡxO → Μb1ЗΧm → ЖkOκΝ4 → ВΚRηn8 → τΔLνtG → δΠ9ωhW → πvXαΒK → Υr5ГΖe → ψfDυΣC → μθbΦRO → ΜΕiΞsm → VPBχκε → μΙwzoO → ΜK2Жοm → ДΤOκe6 → ψΚdΤnC → μfLνΣO → ΠΜbΦli → jXPιβΟ → ΘsUδΕq → xHBχςΑ → μα2ЖYO → ДΜpΗl6 → ψQGςιC → μβΖqXO → ΜsEτΕm → ζPBχκU → μΙyxoO → ΜK0Иοm → ИΤOκe2 → ЖΚdΤn4 → ВfLνΣ8 → τΠbΦhG → δjXαΞW → vrTεΖΓ → zE6Вυy → φη0ИSE → ИθΒuR2 → ЖΕ6Вs4 → ВφBχD8 → τμθQNG → δΝΕrkW → vSCφηΓ → κΓ6ВuQ → φΘ7БpE → τθHρRG → δΩΔsZW → voAψΙΓ → ξK6ВοM → φΤΟheE → θeWβΤS → ΔtdΤΔu → fA8АωΤ → ςοcΥKI → ΩΤgΠea → neYΩΤΛ → peMμΤΙ → ΞeIπΤk → ΧeSζΤc → ΒjdΤΞw → fU4ДεΤ → АycΥyA → πgЙЙΠK → οΡNλgL → ΣΜZΨlg → nbPιΧΛ → ΘkMμΝq → ΞSGςηk → βΓSζuY → Βr7БΖw → τE4ДυG → АηγVSA → πΓuΒuK → Υ86ВБe → φσeΣGE → θγcΥWS → ΔugΠΓu → Z97БАα → τρoΘIG → δΨIπaW → ΧvlΛΒc → jP5ГκΟ → ψΙUδoC → μxJοzO → ΥΜ1Зle → ЖfPιΣ4 → ВΘbΦp8 → τjHρΞG → δΩTεZW → zvnΙΒy → L60ИГο → ИχΡfC2 → ЖλaΧO4 → ВΛkΜm8 → τRNλθG → δΜΔslW → vQAψιΓ → ξΗ6ВqM → φΠFσhE → θδXαVS → ΔwqΖΑu → F93ЕАυ → ВρεTI8 → τΨyxaG → δm0ИΛW → ИvNλΒ2 → ЖΜ5Гl4 → ВψPιB8 → τνΗpMG → δΟGςiW → βvVγΒY → vr5ГΖΓ → ψE6ВυC → φμζSNE → θΝΑvkS → ΔS4Дηu → АΓ8АuA → ςπ7БJI → τΩΥcZG → δogΠΙW → vZJοΩΓ → Υo6ВΙe → φfJοΣE → θΥbΦdS → ΔjfΡΞu → bU8АεΨ → ςykΜyI → ΩQЙЙθa → ιΨ7БaR → τΖlΛrG → δPDυκW → θΙuΒoS → ΔK6Вοu → φΤ8АeE → ςθdΤRI → ΩΕeΣsa → ndBχΥΛ → μgMμΡO → ΞΜZΨlk → nTPιζΛ → ΘΑMμwq → ΞH3Еςk → ВαSζY8 → τΒpΗvG → δH5ГςW → ψαuΒYC → μq6ВΗO → φΜFσlE → θδPιVS → ΘΔvΑtq → HA4Дωσ → АοαXKA → πΤqΖeK → ΥeEτΤe → ζfdΤΣU → zfbΦΣy → jc0ИΦΟ → ИiUδΟ2 → ЖxVγz4 → Вv1ЗΒ8 → Жτ5ГF4 → ВψδUB8 → τνwzMG → δΟ2ЖiW → ДvVγΒ6 → ψv5ГΒC → ψμ5ГNC → ψμΜkNC → μΝQθkO → ΜΖRηrm → ΔPDυκu → θΙ8АoS → ςΔJοtI → ΩΥ9ωda → πnfΡΚK → ΥbLνΧe → ΠkeΣΝi → dXRηβΦ → ΔsgΠΕu → ZC8Аχα → ςλoΘOI → ΩΛIπma → ΧnNλΚc → ΜjLνΞm → ΠUOκεi → ΚyWβyo → tKЙЙξΕ → οΔWβtL → Σt9ωΔg → πb9ωΧK → πΥjΝdK → ΥgSζΡe → ΒfZΨΣw → nc4ДΦΛ → АiMμΟA → πΞVγjK → ΥvTεΒe → zf5ГΣyψc0ИΦCИμhΟN2ЖΝWβk4ВtRηΔ8τΔ9ωtGπδ9ωVKπΥvΑdKΥg4ДΡeАfZΨΣAπnbΦΚKΥjLνΞeΠfTεΣizcWβΦyti0ИΟΕИWAψγ2ЖξtΓL4ВΡ8Аg8τςZΨHGδαmΚYWvqMμΗΓΞG6ВσkφγSζWEθΒtΓvSΔ95ГАuψρ8АICςμΧaNIΩΝkΜkanSQθηΛΖΓMμusΞD7БφkτιSζQGδΗΑvqWvG4ДσΓАγ6ВWAφπtΓJEθΦ8АcSςΔhΟtIΩX9ωβaπsmΚΕKΥNBχμeμΝeΣkOΜdRηΥmΔgOκΡuΚa8АΨoςmKξΛIΩΣNλfaΜnbΦΚmjPLνκΟΠΙUδoixXJοβΑΥs2ЖΕeДfBχΣ6ψμbΦNCμΝiΞkOΜVRηδmΔwOκΑuΚ93ЕАoВρKξI8τΨΡfaGδmaΧΛWvlNλΜΓΜQ6ВιmφΗOκqEθΚFσnSδΔLνtWΠv9ωΒiπX5ГβKψΥrΕdCμgCφΡOκΜZΨlQΘnPιΚqΘMGςνqβΟGςiYβrVγΖYvrDυΖΓθE6ВυSφηΓtSEθΓ8АuSςΔ7БtIτΩ9ωZGπδnΙVKΥwKξΑeΣf3ЕΣgВcaΧΦ8τlhΟΜGδXPιβWΘvrΕΒqHD5ГφσψιαXQCμΗqΖqOΜGEτσmζγOκWUΚztΓxoL91ЗАοЖρΡfI4ВΨaΧa8τmkΜΛGδRNλθWΜΕuΒsmPC6ВχλφλΙnOEθΛKξmSΣΔNλtgΜb9ωΧmπkOκΝKΥΚRηneΔfLνΣuΠc8АΦiςiWβΟIΩtVγΔavn9ωΚΓπM6ВνKφΥΞidEθgUδΡSΔxZΨzun91ЗАΛЖρMμI4ВΨΝja8τmSζΛGδΒNλvWΜv5ГΒmψP5ГκCψμΘoNCμΝIπkOΧΜRηlcΔjPιΞuΘU8АεqςyGςyIβΨЙЙZYαΩ2ЖZZДpnΙΘ6ψLHρξCμΩΠgZOΜoYΩΙmpPJοκΙΥΙIπoeΧfJοΣcΥjbΦΞejfTεΣΟzcUδΦyxi0ИΟΑИW2Жγ2ЖДtΓ54Вω8АA8τςξKHGδαΡfYWvqaΧΗΓlG6ВσΝφγQθWEθΖtΓrSΔE8Аυuςη8АSIςΩΒuZIΩo6ВΙaφnJοΚEθΥLνdSΠΔfΡtibX9ωβΨπskΜΕKΥRBχθeμΕeΣsOΜdBχΥmμgOκΡOΜΚZΨnmnPLνκΛΠΙMμoiΞXJοβkΥsSζΕeΒfBχΣwμc4ДΦOАΜhΟlAπXPιβKΥΘrΕpefICφρΤκΨcΥaQΘmgΠΛqZOGςλαβΛoΘmYrOIπλΗΧΛEτmcζjNλΞUΜzTεxmzP1ЗκyЖΙ0Иo4ИВJο72ЖυΤdE4ВηeΣS8τΓcΥuGδh7БΠWτvXαΒGδr5ГΖWψvDυΒCμθ5ГROψΜΔslCμQAψιOξΜΖqlMΠQEτιiζΗWβqUztFσΔyδA0ИωWИοuΒK2ЖΤ6Вe4ВφdΤD8τιeΣQGδΗcΥqWvhFσΠΓδY6ВαWφvpΗΒEθH5ГςSψαΓtYCμq8АΗOςΜFσlIδΩPιZWΘvnΙΒqLH5ГςοψαΡfYCμqaΧΗOΜlFσΜmδQOκιWΚΗuΒqoLG6ВσοφγΡfWEθuaΧΓSΔl7БΜuτQ8АιGςδΖqVIΩwEτΑaζn3ЕΚUВzLνx8τΠ1ЗhGЖδXαV4ВwqΖΑ8τF3ЕτGВεγVU8τyuΒyGδ6ЙЙВWГγNλW7φΜtΓlEθQ8АιSςΗΓtqIΩG8АσaςγmΚWIΩuMμΓaΞn7БΚkτTLνζGδΠzwhWvY2ЖαΓДq6ВΗ6ψφFσDCμιγVQOΜΗuΒqmPG6ВσλφγΙnWEθuKξΓSΣΔ7Бtgτb9ωΧGπδjΝVKΥwSζΑeΒf3ЕΣwВc4ДΦ8АτhΟFAπεWβUKΥysΔyefAЙЙψΤωΣSζfBξΒbΦvMΠj5ГΞiψXTεβCμzrΕxOΜD1ЗφmЖιOκQ4ВΚΖqn8τMEτνGζδΞiVUzwUδΑyx40ИЕΑИБ2Ж82ЖДςG54ВωαXA8τοqΖKGδΤEτeWζvdΤΒUzf5ГΣy