Base 211: 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
24 max steps10 → 0ツ → ッ1 → チ3 → ソ7
3106 max steps100 → 0ツツ → ッツ1 → ヂツ2 → チツ3 → ダツ4 → タツ5 → ゾツ6 → ソツ7 → ゼツ8 → セツ9 → ズツA → スツB → ジツC → シツD → ザツE → サツF → ゴツG → コツH → ゲツI → ケツJ → グツK → クツL → ギツM → キツN → ガツO → カツP → オツQ → ォツR → エツS → ェツT → ウツU → ゥツV → イツW → ィツX → アツY → ァツZ → яツa → юツb → эツc → ьツd → ыツe → ъツf → щツg → шツh → чツi → цツj → хツk → фツl → уツm → тツn → сツo → рツp → пツq → оツr → нツs → мツt → лツu → кツv → йツw → иツx → зツy → жツz → еツΑ → дツΒ → гツΓ → вツΔ → бツΕ → аツΖ → ЯツΗ → ЮツΘ → ЭツΙ → ЬツΚ → ЫツΛ → ЪツΜ → ЩツΝ → ШツΞ → ЧツΟ → ЦツΠ → ХツΡ → ФツΣ → УツΤ → ТツΥ → СツΦ → РツΧ → ПツΨ → ОツΩ → Нツα → Мツβ → Лツγ → Кツδ → Йツε → Иツζ → Зツη → Жツθ → Еツι → Дツκ → Гツλ → Вツμ → Бツν → Аツξ → ωツο → ψツπ → χツρ → φツς → υツσ → τツτ
44 max stepsυ000 → τツツτ → τστυ → 1ツツッ → ッ0ッ2
578 max steps1000C → C0ツッス → ツザツD1 → ッザツD2 → ヂサツE3 → チコツG4 → ダグツJ5 → タガツN6 → ゾェツS7 → ソァツY8 → ゼщツf9 → セсツnA → ズиツwB → スЮツΗC → ジУツΣD → シЗツζE → ザτツσF → サζツЗG → ゴςツυH → コεツИI → ゲρツφJ → ケδツЙK → グπツχL → クγツКM → ギοツψN → キβツЛO → ガξツωP → カαツМQ → オνツАR → ォΩツНS → エμツБT → ェΨツОU → ウλツВV → ゥΧツПW → イκツГX → ィΦツРY → アιツДZ → ァΥツСa → яθツЕb → юΤツТc → эηツЖd → ьΣツУe → ыζツЗf → ъΡツФg → щεツИh → шΠツХi → чδツЙj → цΟツЦk → хγツКl → фΞツЧm → уβツЛn → тΝツШo → сαツМp → рΜツЩq → пΩツНr → оΛツЪs → нΨツОt → мΚツЫu → лΧツПv → кΙツЬw → йΦツРx → иΘツЭy → зΥツСz → жΗツЮΑ → еΤツТΒ → дΖツЯΓ → гΣツУΔ → вΕツаΕ → бΡツФΖ → аΔツбΗ → вΞツЧΕ → бΘツЭΖ → аΝツШΗ → ЯΗツЮΘ → ЯΛツЪΘ → ЮΘツЭΙ → ЮΙツЬΙ → ЭΙツЬΚ → ЭΗツЮΚ