Base 213: 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
23 max steps10 → 0テ → ヅ1 → ッ3
3107 max steps100 → 0テテ → ヅテ1 → ツテ2 → ッテ3 → ヂテ4 → チテ5 → ダテ6 → タテ7 → ゾテ8 → ソテ9 → ゼテA → セテB → ズテC → ステD → ジテE → シテF → ザテG → サテH → ゴテI → コテJ → ゲテK → ケテL → グテM → クテN → ギテO → キテP → ガテQ → カテR → オテS → ォテT → エテU → ェテV → ウテW → ゥテX → イテY → ィテZ → アテa → ァテb → яテc → юテd → эテe → ьテf → ыテg → ъテh → щテi → шテj → чテk → цテl → хテm → фテn → уテo → тテp → сテq → рテr → пテs → оテt → нテu → мテv → лテw → кテx → йテy → иテz → зテΑ → жテΒ → еテΓ → дテΔ → гテΕ → вテΖ → бテΗ → аテΘ → ЯテΙ → ЮテΚ → ЭテΛ → ЬテΜ → ЫテΝ → ЪテΞ → ЩテΟ → ШテΠ → ЧテΡ → ЦテΣ → ХテΤ → ФテΥ → УテΦ → ТテΧ → СテΨ → РテΩ → Пテα → Оテβ → Нテγ → Мテδ → Лテε → Кテζ → Йテη → Иテθ → Зテι → Жテκ → Еテλ → Дテμ → Гテν → Вテξ → Бテο → Аテπ → ωテρ → ψテς → χテσ → φテτ → υテυ
44 max stepsφ000 → υテテυ → υτυφ → 1テテヅ → ヅ0ヅ2
582 max steps10000 → 0テテテテ → ヅテテテ1 → ヅ0テヅ2 → テヂテ31 → ヅヂテ32 → ツチテ43 → ッタテ64 → ヂゼテ95 → チジテD6 → ダコテI7 → タキテO8 → ゾウテV9 → ソэテdA → ゼфテmB → セкテwC → ズЯテΘD → スУテΥE → ジЖテιF → シςテχG → ザθテЗH → サρテψI → ゴηテИJ → コπテωK → ゲζテЙL → ケοテАM → グεテКN → クξテБO → ギδテЛP → キνテВQ → ガγテМR → カμテГS → オβテНT → ォλテДU → エαテОV → ェκテЕW → ウΩテПX → ゥιテЖY → イΨテРZ → ィθテЗa → アΧテСb → ァηテИc → яΦテТd → юζテЙe → эΥテУf → ьεテКg → ыΤテФh → ъδテЛi → щΣテХj → шγテМk → чΡテЦl → цβテНm → хΠテЧn → фαテОo → уΟテШp → тΩテПq → сΞテЩr → рΨテРs → пΝテЪt → оΧテСu → нΜテЫv → мΦテТw → лΛテЬx → кΥテУy → йΚテЭz → иΤテФΑ → зΙテЮΒ → жΣテХΓ → еΘテЯΔ → дΡテЦΕ → гΗテаΖ → вΠテЧΗ → бΖテбΘ → вΝテЪΗ → бΙテЮΘ → аΜテЫΙ → ЯΘテЯΚ → аΙテЮΙ → ЯΛテЬΚ → ЮΘテЯΛ → аΘテЯΙ → аΛテЬΙ → ЯΙテЮΚ