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 steps1 → 0 → 0
233 max steps10 → 0Й → И1 → Ж3 → В7 → τF → δV → vΒ → 5Д → ψB → μN → Μl → Pκ → Θp → Hς → ΩZ → nΚ → Lξ → Πh → Xβ → rΖ → Dφ → θR → Δt → 9А → πJ → Υd → fΣ → bΧ → jΞ → Tζ → zx → 1И → Ж3
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 → yЙy → xЙz → yЙy
459 max stepsz000 → yЙЙy → yxyz → 1ЙЙИ → И0И2 → ИЕ32 → ЖБ74 → ВσF8 → τγVG → δuΒW → v6ВΓ → φ6ВE → φηRE → θΓtS → Δ8Аu → ς8АI → ςΨZI → ΩmΚa → nMμΛ → ΞMμk → ΞSζk → ΒSζw → Β4Дw → А4ДA → АοJA → πΤdK → ΥeΣe → fcΥΤ → hcΥΡ → hYΩΡ → pYΩΙ → pIπΙ → ΧIπc → ΧiΞc → jUδΟ → xUδΑ → x2ЖΑ → Д2Ж6 → ДχB6 → ψλNC → μΛlO → ΜOκm → ΚOκo → ΚKξo → ΣKξg → ΣaΧg → laΧΝ → lQθΝ → ΖQθs → ΖCφs → κCφQ → κΗpQ → ΘGςq → βGςY → βqΖY → rEτΗ → ζEτU → ζyxU → z0Иy → И0И2
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 → ΤcЙΥf → ΦdЙΤd → ΥgЙΠe → ΤcЙΥf
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 → zf5ГΣy → ψc0ИΦC → ИμhΟN2 → ЖΝWβk4 → ВtRηΔ8 → τΔ9ωtG → πδ9ωVK → πΥvΑdK → Υg4ДΡe → АfZΨΣA → πnbΦΚK → ΥjLνΞe → ΠfTεΣi → zcWβΦy → ti0ИΟΕ → ИWAψγ2 → ЖξtΓL4 → ВΡ8Аg8 → τςZΨHG → δαmΚYW → vqMμΗΓ → ΞG6Вσk → φγSζWE → θΒtΓvS → Δ95ГАu → ψρ8АIC → ςμΧaNI → ΩΝkΜka → nSQθηΛ → ΖΓMμus → ΞD7Бφk → τιSζQG → δΗΑvqW → vG4ДσΓ → Аγ6ВWA → φπtΓJE → θΦ8АcS → ςΔhΟtI → ΩX9ωβa → πsmΚΕK → ΥNBχμe → μΝeΣkO → ΜdRηΥm → ΔgOκΡu → Κa8АΨo → ςmKξΛI → ΩΣNλfa → ΜnbΦΚm → jPLνκΟ → ΠΙUδoi → xXJοβΑ → Υs2ЖΕe → ДfBχΣ6 → ψμbΦNC → μΝiΞkO → ΜVRηδm → ΔwOκΑu → Κ93ЕАo → ВρKξI8 → τΨΡfaG → δmaΧΛW → vlNλΜΓ → ΜQ6Вιm → φΗOκqE → θΚFσnS → δΔLνtW → Πv9ωΒi → πX5ГβK → ψΥrΕdC → μgCφΡO → κΜZΨlQ → ΘnPιΚq → ΘMGςνq → βΟGςiY → βrVγΖY → vrDυΖΓ → θE6ВυS → φηΓtSE → θΓ8АuS → ςΔ7БtI → τΩ9ωZG → πδnΙVK → ΥwKξΑe → Σf3ЕΣg → ВcaΧΦ8 → τlhΟΜG → δXPιβW → ΘvrΕΒq → HD5Гφσ → ψιαXQC → μΗqΖqO → ΜGEτσm → ζγOκWU → ΚztΓxo → L91ЗАο → ЖρΡfI4 → ВΨaΧa8 → τmkΜΛG → δRNλθW → ΜΕuΒsm → PC6Вχλ → φλΙnOE → θΛKξmS → ΣΔNλtg → Μb9ωΧm → πkOκΝK → ΥΚRηne → ΔfLνΣu → Πc8АΦi → ςiWβΟI → ΩtVγΔa → vn9ωΚΓ → πM6ВνK → φΥΞidE → θgUδΡS → ΔxZΨzu → n91ЗАΛ → ЖρMμI4 → ВΨΝja8 → τmSζΛG → δΒNλvW → Μv5ГΒm → ψP5ГκC → ψμΘoNC → μΝIπkO → ΧΜRηlc → ΔjPιΞu → ΘU8Аεq → ςyGςyI → βΨЙЙZY → αΩ2ЖZZ → ДpnΙΘ6 → ψLHρξC → μΩΠgZO → ΜoYΩΙm → pPJοκΙ → ΥΙIπoe → ΧfJοΣc → ΥjbΦΞe → jfTεΣΟ → zcUδΦy → xi0ИΟΑ → ИW2Жγ2 → ЖДtΓ54 → Вω8АA8 → τςξKHG → δαΡfYW → vqaΧΗΓ → lG6ВσΝ → φγQθWE → θΖtΓrS → ΔE8Аυu → ςη8АSI → ςΩΒuZI → Ωo6ВΙa → φnJοΚE → θΥLνdS → ΠΔfΡti → bX9ωβΨ → πskΜΕK → ΥRBχθe → μΕeΣsO → ΜdBχΥm → μgOκΡO → ΜΚZΨnm → nPLνκΛ → ΠΙMμoi → ΞXJοβk → ΥsSζΕe → ΒfBχΣw → μc4ДΦO → АΜhΟlA → πXPιβK → ΥΘrΕpe → fICφρΤ → κΨcΥaQ → ΘmgΠΛq → ZOGςλα → βΛoΘmY → rOIπλΗ → ΧΛEτmc → ζjNλΞU → ΜzTεxm → zP1Зκy → ЖΙ0Иo4 → ИВJο72 → ЖυΤdE4 → ВηeΣS8 → τΓcΥuG → δh7БΠW → τvXαΒG → δr5ГΖW → ψvDυΒC → μθ5ГRO → ψΜΔslC → μQAψιO → ξΜΖqlM → ΠQEτιi → ζΗWβqU → ztFσΔy → δA0ИωW → ИοuΒK2 → ЖΤ6Вe4 → ВφdΤD8 → τιeΣQG → δΗcΥqW → vhFσΠΓ → δY6ВαW → φvpΗΒE → θH5ГςS → ψαΓtYC → μq8АΗO → ςΜFσlI → δΩPιZW → ΘvnΙΒq → LH5Гςο → ψαΡfYC → μqaΧΗO → ΜlFσΜm → δQOκιW → ΚΗuΒqo → LG6Вσο → φγΡfWE → θuaΧΓS → Δl7БΜu → τQ8АιG → ςδΖqVI → ΩwEτΑa → ζn3ЕΚU → ВzLνx8 → τΠ1ЗhG → ЖδXαV4 → ВwqΖΑ8 → τF3ЕτG → ВεγVU8 → τyuΒyG → δ6ЙЙВW → ГγNλW7 → φΜtΓlE → θQ8АιS → ςΗΓtqI → ΩG8Аσa → ςγmΚWI → ΩuMμΓa → Ξn7БΚk → τTLνζG → δΠzwhW → vY2ЖαΓ → Дq6ВΗ6 → ψφFσDC → μιγVQO → ΜΗuΒqm → PG6Вσλ → φγΙnWE → θuKξΓS → ΣΔ7Бtg → τb9ωΧG → πδjΝVK → ΥwSζΑe → Βf3ЕΣw → Вc4ДΦ8 → АτhΟFA → πεWβUK → ΥysΔye → fAЙЙψΤ → ωΣSζfB → ξΒbΦvM → Πj5ГΞi → ψXTεβC → μzrΕxO → ΜD1Зφm → ЖιOκQ4 → ВΚΖqn8 → τMEτνG → ζδΞiVU → zwUδΑy → x40ИЕΑ → ИБ2Ж82 → ЖДςG54 → ВωαXA8 → τοqΖKG → δΤEτeW → ζvdΤΒU → zf5ГΣy