Base 199: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР
СТУФХЦЧШЩЪЫЬЭЮЯа
бвгдежзийклмнопр
стуфхцчшщъыьэюяァ
アィイゥウェエォオカガキギクグケ
ゲコゴサザシジスズセゼソゾタダチ

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
215 max steps10 → 0ジ → シ1 → サ3 → ケ7 → ォF → шV → ШΒ → ΚР → tа → βА → Nァ → иl → ςκ → 7ケ → ォF
3102 max steps100 → 0ジジ → シジ1 → ザジ2 → サジ3 → ゴジ4 → コジ5 → ゲジ6 → ケジ7 → グジ8 → クジ9 → ギジA → キジB → ガジC → カジD → オジE → ォジF → エジG → ェジH → ウジI → ゥジJ → イジK → ィジL → アジM → ァジN → яジO → юジP → эジQ → ьジR → ыジS → ъジT → щジU → шジV → чジW → цジX → хジY → фジZ → уジa → тジb → сジc → рジd → пジe → оジf → нジg → мジh → лジi → кジj → йジk → иジl → зジm → жジn → еジo → дジp → гジq → вジr → бジs → аジt → Яジu → Юジv → Эジw → Ьジx → Ыジy → Ъジz → ЩジΑ → ШジΒ → ЧジΓ → ЦジΔ → ХジΕ → ФジΖ → УジΗ → ТジΘ → СジΙ → РジΚ → ПジΛ → ОジΜ → НジΝ → МジΞ → ЛジΟ → КジΠ → ЙジΡ → ИジΣ → ЗジΤ → ЖジΥ → ЕジΦ → ДジΧ → ГジΨ → ВジΩ → Бジα → Аジβ → ωジγ → ψジδ → χジε → φジζ → υジη → τジθ → σジι → ςジκ → ρジλ → πジμ → οジν → ξジξ → νジο → ξジξ
4103 max stepsο000 → ξジジξ → ξνξο → 1ジジシ → シ0シ2 → シゴ32 → サグ74 → ケエF8 → ォчVG → шЧΒW → ШΙРΓ → ΚuЮС → ΩuЮГ → ΩSъГ → ЮSъw → ЮΦДw → ΧWцЕ → ЦWцΕ → ЦΕФΕ → ΖΓЦХ → ΘΓЦУ → ΘyЪУ → ΠyЪЛ → ΠiкЛ → ψiкε → ψIゥε → тIゥc → тЛΞc → МkиΟ → τkиι → τAキι → ィAキM → ィлhM → мωβi → АMァγ → кMァk → кυζk → φEォη → ъEォU → ъЫxU → ЬΡИy → ΣeоЙ → ЖeоΦ → ЖYфΦ → ТYфΙ → ТwЬΙ → ΥwЬЗ → ΥaтЗ → ОaтΝ → ОoдΝ → μoдρ → μ4コρ → ク4コA → クイJA → ゥпdK → рЗΣe → ИcрΤ → КcрΡ → КgмΡ → Вgмα → ВQьα → вQьs → вεφs → ζGェχ → цGェY → цУΖY → ФΑШΗ → ΜΑШП → ΜqвП → θqвυ → θCカυ → юCカQ → югpQ → дιςq → κ8クσ → ェ8クI → ェуZI → фПΚa → РsаΛ → δsаω → δKィω → оKィg → оГΧg → ДUшΨ → ЪUшΑ → ЪΝМΑ → ΞmжН → πmжν → π2サν → コ2サ6 → コガB6 → キяNC → ァзlO → иρκm → ς6ケλ → カ6ケE → カыRE → ьЯtS → аαАu → βOюБ → жOюo → жνξo → ξ0シο → シ0シ2
577 max steps10006 → 60ジシコ → ジグジ71 → シグジ72 → ザクジ83 → サキジA4 → ゴオジD5 → コウジH6 → ゲァジM7 → ケъジS8 → グуジZ9 → クлジhA → ギвジqB → キШジΑC → ガНジΜD → カБジΩE → オξジνF → ォΩジБG → エμジοH → ェΨジВI → ウλジπJ → ゥΧジГK → イκジρL → ィΦジДM → アιジςN → ァΥジЕO → яθジσP → юΤジЖQ → эηジτR → ьΣジЗS → ыζジυT → ъΡジИU → щεジφV → шΠジЙW → чδジχX → цΟジКY → хγジψZ → фΞジЛa → уβジωb → тΝジМc → сαジАd → рΜジНe → пΩジБf → оΛジОg → нΨジВh → мΚジПi → лΧジГj → кΙジРk → йΦジДl → иΘジСm → зΥジЕn → жΗジТo → еΤジЖp → дΖジУq → гΣジЗr → вΕジФs → бΡジИt → аΔジХu → ЯΠジЙv → ЮΓジЦw → ЭΟジКx → ЬΒジЧy → ЫΞジЛz → ЪΑジШΑ → ЩΝジМΒ → ШzジЩΓ → ЪΚジПΑ → ЩΔジХΒ → ШΙジРΓ → ЧΓジЦΔ → ЧΗジТΔ → ЦΔジХΕ → ЦΕジФΕ → ХΕジФΖ → ХΓジЦΖ → ЧΔジХΔ → ЦΗジТΕ → ХΓジЦΖ