Base 201: 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

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 steps10
23 max steps10 → 0ズ → ス1 → シ3
3101 max steps100 → 0ズズ → スズ1 → ジズ2 → シズ3 → ザズ4 → サズ5 → ゴズ6 → コズ7 → ゲズ8 → ケズ9 → グズA → クズB → ギズC → キズD → ガズE → カズF → オズG → ォズH → エズI → ェズJ → ウズK → ゥズL → イズM → ィズN → アズO → ァズP → яズQ → юズR → эズS → ьズT → ыズU → ъズV → щズW → шズX → чズY → цズZ → хズa → фズb → уズc → тズd → сズe → рズf → пズg → оズh → нズi → мズj → лズk → кズl → йズm → иズn → зズo → жズp → еズq → дズr → гズs → вズt → бズu → аズv → Яズw → Юズx → Эズy → Ьズz → ЫズΑ → ЪズΒ → ЩズΓ → ШズΔ → ЧズΕ → ЦズΖ → ХズΗ → ФズΘ → УズΙ → ТズΚ → СズΛ → РズΜ → ПズΝ → ОズΞ → НズΟ → МズΠ → ЛズΡ → КズΣ → ЙズΤ → ИズΥ → ЗズΦ → ЖズΧ → ЕズΨ → ДズΩ → Гズα → Вズβ → Бズγ → Аズδ → ωズε → ψズζ → χズη → φズθ → υズι → τズκ → σズλ → ςズμ → ρズν → πズξ → οズο
44 max stepsπ000 → οズズο → οξοπ → 1ズズス → ス0ス2
577 max steps10007 → 70ズスゴ → ズケズ81 → スケズ82 → ジグズ93 → シギズB4 → ザカズE5 → サェズI6 → ゴアズN7 → コыズT8 → ゲфズa9 → ケмズiA → グгズrB → クЩズΒC → ギОズΝD → キВズαE → ガοズξF → カαズВG → オνズπH → ォΩズГI → エμズρJ → ェΨズДK → ウλズςL → ゥΧズЕM → イκズσN → ィΦズЖO → アιズτP → ァΥズЗQ → яθズυR → юΤズИS → эηズφT → ьΣズЙU → ыζズχV → ъΡズКW → щεズψX → шΠズЛY → чδズωZ → цΟズМa → хγズАb → фΞズНc → уβズБd → тΝズОe → сαズВf → рΜズПg → пΩズГh → оΛズРi → нΨズДj → мΚズСk → лΧズЕl → кΙズТm → йΦズЖn → иΘズУo → зΥズЗp → жΗズФq → еΤズИr → дΖズХs → гΣズЙt → вΕズЦu → бΡズКv → аΔズЧw → ЯΠズЛx → ЮΓズШy → ЭΟズМz → ЬΒズЩΑ → ЫΞズНΒ → ЪΑズЪΓ → ЫΛズРΒ → ЪΔズЧΓ → ЩΚズСΔ → ШΓズШΕ → ЩΗズФΔ → ШΖズХΕ → ЧΖズХΖ → ЦΕズЦΗ → ЧΓズШΖ → ЩΖズХΔ → ШΗズФΕ → ЧΕズЦΖ