Base 161: 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

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 → 0с → р1 → о3
381 max steps100 → 0сс → рс1 → пс2 → ос3 → нс4 → мс5 → лс6 → кс7 → йс8 → ис9 → зсA → жсB → есC → дсD → гсE → всF → бсG → асH → ЯсI → ЮсJ → ЭсK → ЬсL → ЫсM → ЪсN → ЩсO → ШсP → ЧсQ → ЦсR → ХсS → ФсT → УсU → ТсV → СсW → РсX → ПсY → ОсZ → Нсa → Мсb → Лсc → Ксd → Йсe → Исf → Зсg → Жсh → Есi → Дсj → Гсk → Всl → Бсm → Асn → ωсo → ψсp → χсq → φсr → υсs → τсt → σсu → ςсv → ρсw → πсx → οсy → ξсz → νсΑ → μсΒ → λсΓ → κсΔ → ιсΕ → θсΖ → ηсΗ → ζсΘ → εсΙ → δсΚ → γсΛ → βсΜ → αсΝ → ΩсΞ → ΨсΟ → ΧсΠ → ΦсΡ → ΥсΣ → ΤсΤ
44 max stepsΥ000 → ΤссΤ → ΤΣΤΥ → 1сср → р0р2
559 max stepsΣ0000 → ΡсссΦ → ΦΠсΦΣ → Χ2соΡ → пΡсΥ3 → оΣсΤ4 → нΠсΦ5 → мΡсΥ6 → лΟсΧ7 → кΠсΦ8 → йΞсΨ9 → иΟсΧA → зΝсΩB → жΞсΨC → еΜсαD → дΝсΩE → гΛсβF → вΜсαG → бΚсγH → аΛсβI → ЯΙсδJ → ЮΚсγK → ЭΘсεL → ЬΙсδM → ЫΗсζN → ЪΘсεO → ЩΖсηP → ШΗсζQ → ЧΕсθR → ЦΖсηS → ХΔсιT → ФΕсθU → УΓсκV → ТΔсιW → СΒсλX → РΓсκY → ПΑсμZ → ОΒсλa → Нzсνb → МΑсμc → Лyсξd → Кzсνe → Йxсοf → Иyсξg → Зwсπh → Жxсοi → Еvсρj → Дwсπk → Гuсςl → Вvсρm → Бtсσn → Аuсςo → ωsсτp → ψtсσq → χrсυr → φsсτs → υqсφt → χpсχr → ψsсτq → χsсτr