Base 205: 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
254 max steps10 → 0ゾ → ソ1 → セ3 → シ7 → クF → юV → ЮΒ → ΠР → nм → τξ → 5ス → コB → ェN → оl → ψκ → Dケ → ィR → жt → θА → Hキ → ъZ → ЦΚ → zа → ΥМ → fф → КΧ → bш → ТΞ → rи → μφ → 9サ → カJ → цd → ОΣ → jр → Вζ → Lォ → тh → Жβ → Tァ → вx → ΩИ → Xь → ЪΖ → ΘШ → ΔЬ → ΜФ → vд → δД → Pゥ → кp → πς → 1ソ → セ3
3105 max steps100 → 0ゾゾ → ソゾ1 → ゼゾ2 → セゾ3 → ズゾ4 → スゾ5 → ジゾ6 → シゾ7 → ザゾ8 → サゾ9 → ゴゾA → コゾB → ゲゾC → ケゾD → グゾE → クゾF → ギゾG → キゾH → ガゾI → カゾJ → オゾK → ォゾL → エゾM → ェゾN → ウゾO → ゥゾP → イゾQ → ィゾR → アゾS → ァゾT → яゾU → юゾV → эゾW → ьゾX → ыゾY → ъゾZ → щゾa → шゾb → чゾc → цゾd → хゾe → фゾf → уゾg → тゾh → сゾi → рゾj → пゾk → оゾl → нゾm → мゾn → лゾo → кゾp → йゾq → иゾr → зゾs → жゾt → еゾu → дゾv → гゾw → вゾx → бゾy → аゾz → ЯゾΑ → ЮゾΒ → ЭゾΓ → ЬゾΔ → ЫゾΕ → ЪゾΖ → ЩゾΗ → ШゾΘ → ЧゾΙ → ЦゾΚ → ХゾΛ → ФゾΜ → УゾΝ → ТゾΞ → СゾΟ → РゾΠ → ПゾΡ → ОゾΣ → НゾΤ → МゾΥ → ЛゾΦ → КゾΧ → ЙゾΨ → ИゾΩ → Зゾα → Жゾβ → Еゾγ → Дゾδ → Гゾε → Вゾζ → Бゾη → Аゾθ → ωゾι → ψゾκ → χゾλ → φゾμ → υゾν → τゾξ → σゾο → ςゾπ → ρゾρ → πゾς → ρゾρ
414 max stepsς000 → ρゾゾρ → ρπρς → 1ゾゾソ → ソ0ソ2 → ソズ32 → セザ74 → シギF8 → クэVG → юЭΒW → ЮΟРΓ → ΠoкС → ςoкρ → ς0ソρ → ソ0ソ2
579 max steps10009 → 90ゾソザ → ゾコゾA1 → ソコゾA2 → ゼゲゾB3 → セグゾD4 → ズキゾG5 → スォゾK6 → ジイゾP7 → シэゾV8 → ザцゾc9 → サоゾkA → ゴеゾtB → コЫゾΔC → ゲРゾΟD → ケДゾγE → グρゾπF → クγゾДG → ギοゾςH → キβゾЕI → ガξゾσJ → カαゾЖK → オνゾτL → ォΩゾЗM → エμゾυN → ェΨゾИO → ウλゾφP → ゥΧゾЙQ → イκゾχR → ィΦゾКS → アιゾψT → ァΥゾЛU → яθゾωV → юΤゾМW → эηゾАX → ьΣゾНY → ыζゾБZ → ъΡゾОa → щεゾВb → шΠゾПc → чδゾГd → цΟゾРe → хγゾДf → фΞゾСg → уβゾЕh → тΝゾТi → сαゾЖj → рΜゾУk → пΩゾЗl → оΛゾФm → нΨゾИn → мΚゾХo → лΧゾЙp → кΙゾЦq → йΦゾКr → иΘゾЧs → зΥゾЛt → жΗゾШu → еΤゾМv → дΖゾЩw → гΣゾНx → вΕゾЪy → бΡゾОz → аΔゾЫΑ → ЯΠゾПΒ → ЮΓゾЬΓ → ЭΟゾРΔ → ЬΒゾЭΕ → ЮΜゾУΓ → ЭΖゾЩΔ → ЬΛゾФΕ → ЫΕゾЪΖ → ЫΙゾЦΖ → ЪΖゾЩΗ → ЪΗゾШΗ → ЩΗゾШΘ → ЩΕゾЪΘ → ЫΖゾЩΖ → ЪΙゾЦΗ → ЩΕゾЪΘ