Base 218: Maximum Iteration Sequences: Cycle Start

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
ヂッツヅテデトドナニヌネノハバパ

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
Cycle Start
11 max steps1 → 0
22 max steps20 → 1ナ → ト3
3110 max steps100 → 0ニニ → ナニ1 → ドニ2 → トニ3 → デニ4 → テニ5 → ヅニ6 → ツニ7 → ッニ8 → ヂニ9 → チニA → ダニB → タニC → ゾニD → ソニE → ゼニF → セニG → ズニH → スニI → ジニJ → シニK → ザニL → サニM → ゴニN → コニO → ゲニP → ケニQ → グニR → クニS → ギニT → キニU → ガニV → カニW → オニX → ォニY → エニZ → ェニa → ウニb → ゥニc → イニd → ィニe → アニf → ァニg → яニh → юニi → эニj → ьニk → ыニl → ъニm → щニn → шニo → чニp → цニq → хニr → фニs → уニt → тニu → сニv → рニw → пニx → оニy → нニz → мニΑ → лニΒ → кニΓ → йニΔ → иニΕ → зニΖ → жニΗ → еニΘ → дニΙ → гニΚ → вニΛ → бニΜ → аニΝ → ЯニΞ → ЮニΟ → ЭニΠ → ЬニΡ → ЫニΣ → ЪニΤ → ЩニΥ → ШニΦ → ЧニΧ → ЦニΨ → ХニΩ → Фニα → Уニβ → Тニγ → Сニδ → Рニε → Пニζ → Оニη → Нニθ → Мニι → Лニκ → Кニλ → Йニμ → Иニν → Зニξ → Жニο → Еニπ → Дニρ → Гニς → Вニσ → Бニτ → Аニυ → ωニφ → ψニχ → χニψ
47 max stepsR00Φ → ΦQグЩ → хrфs → Аχχφ → 3ニニト → ト2ト4 → テッ76 → ダセFC
580 max steps10000 → 0ニニニニ → ナニニニ1 → ナ0ニナ2 → ニデニ31 → ナデニ32 → ドテニ43 → トツニ64 → デチニ95 → テソニD6 → ヅジニI7 → ツゲニO8 → ッカニV9 → ヂィニdA → チщニmB → ダпニwC → タдニΘD → ゾШニΥE → ソЛニιF → ゼχニχG → セθニМH → ズφニψI → スηニНJ → ジυニωK → シζニОL → ザτニАM → サεニПN → ゴσニБO → コδニРP → ゲςニВQ → ケγニСR → グρニГS → クβニТT → ギπニДU → キαニУV → ガοニЕW → カΩニФX → オξニЖY → ォΨニХZ → エνニЗa → ェΧニЦb → ウμニИc → ゥΦニЧd → イλニЙe → ィΥニШf → アκニКg → ァΤニЩh → яιニЛi → юΣニЪj → эθニМk → ьΡニЫl → ыηニНm → ъΠニЬn → щζニОo → шΟニЭp → чεニПq → цΞニЮr → хδニРs → фΝニЯt → уγニСu → тΜニаv → сβニТw → рΛニбx → пαニУy → оΚニвz → нΩニФΑ → мΙニгΒ → лΨニХΓ → кΘニдΔ → йΧニЦΕ → иΗニеΖ → зΦニЧΗ → жΖニжΘ → зΣニЪΗ → жΙニгΘ → еΡニЫΙ → дΘニдΚ → еΞニЮΙ → дΛニбΚ → гΝニЯΛ → вΚニвΜ