Base 219: 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
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
Full Cycle
12 max steps1 → 0 → 0
224 max steps10 → 0ヌ → ニ1 → ド3 → ヅ7 → ソF → キV → мΒ → ζР → Zォ → дΚ → Ξа → Ζи → ΧШ → pш → Дς → Bチ → サN → ьl → Мκ → Rケ → фt → φА → 3ド → ヅ7
3112 max steps100 → 0ヌヌ → ニヌ1 → ナヌ2 → ドヌ3 → トヌ4 → デヌ5 → テヌ6 → ヅヌ7 → ツヌ8 → ッヌ9 → ヂヌA → チヌB → ダヌC → タヌD → ゾヌE → ソヌF → ゼヌG → セヌH → ズヌI → スヌJ → ジヌK → シヌL → ザヌM → サヌN → ゴヌO → コヌP → ゲヌQ → ケヌR → グヌS → クヌT → ギヌU → キヌV → ガヌW → カヌX → オヌY → ォヌZ → エヌa → ェヌb → ウヌc → ゥヌd → イヌe → ィヌf → アヌg → ァヌh → яヌi → юヌj → эヌk → ьヌl → ыヌm → ъヌn → щヌo → шヌp → чヌq → цヌr → хヌs → фヌt → уヌu → тヌv → сヌw → рヌx → пヌy → оヌz → нヌΑ → мヌΒ → лヌΓ → кヌΔ → йヌΕ → иヌΖ → зヌΗ → жヌΘ → еヌΙ → дヌΚ → гヌΛ → вヌΜ → бヌΝ → аヌΞ → ЯヌΟ → ЮヌΠ → ЭヌΡ → ЬヌΣ → ЫヌΤ → ЪヌΥ → ЩヌΦ → ШヌΧ → ЧヌΨ → ЦヌΩ → Хヌα → Фヌβ → Уヌγ → Тヌδ → Сヌε → Рヌζ → Пヌη → Оヌθ → Нヌι → Мヌκ → Лヌλ → Кヌμ → Йヌν → Иヌξ → Зヌο → Жヌπ → Еヌρ → Дヌς → Гヌσ → Вヌτ → Бヌυ → Аヌφ → ωヌχ → ψヌψ → χヌω → ψヌψ
422 max stepsω000 → ψヌヌψ → ψχψω → 1ヌヌニ → ニ0ニ2 → ニト32 → ドツ74 → ヅゼF8 → ソガVG → キлΒW → мεРΓ → ζaェС → вaェΝ → вΙдΝ → ΠΙдЯ → ΠΓкЯ → δΓкУ → δeィУ → ЪeィΦ → ЪsфΦ → ψsфω → ψ0ニω → ニ0ニ2
584 max steps1000G → G0ヌニソ → ヌズヌH1 → ニズヌH2 → ナスヌI3 → ドシヌK4 → トゴヌN5 → デグヌR6 → テカヌW7 → ヅゥヌc8 → ツэヌj9 → ッхヌrA → ヂмヌΑB → チвヌΛC → ダЧヌΧD → タЛヌκE → ゾψヌχF → ソκヌЛG → ゼφヌωH → セιヌМI → ズυヌАJ → スθヌНK → ジτヌБL → シηヌОM → ザσヌВN → サζヌПO → ゴςヌГP → コεヌРQ → ゲρヌДR → ケδヌСS → グπヌЕT → クγヌТU → ギοヌЖV → キβヌУW → ガξヌЗX → カαヌФY → オνヌИZ → ォΩヌХa → エμヌЙb → ェΨヌЦc → ウλヌКd → ゥΧヌЧe → イκヌЛf → ィΦヌШg → アιヌМh → ァΥヌЩi → яθヌНj → юΤヌЪk → эηヌОl → ьΣヌЫm → ыζヌПn → ъΡヌЬo → щεヌРp → шΠヌЭq → чδヌСr → цΟヌЮs → хγヌТt → фΞヌЯu → уβヌУv → тΝヌаw → сαヌФx → рΜヌбy → пΩヌХz → оΛヌвΑ → нΨヌЦΒ → мΚヌгΓ → лΧヌЧΔ → кΙヌдΕ → йΦヌШΖ → иΘヌеΗ → зΥヌЩΘ → жΗヌжΙ → зΡヌЬΘ → жΚヌгΙ → еΠヌЭΚ → дΙヌдΛ → еΝヌаΚ → дΜヌбΛ → гΜヌбΜ → вΛヌвΝ → гΙヌдΜ → еΜヌбΚ → дΝヌаΛ → гΛヌвΜ → гΛヌвΜ