Base 172: 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
22 max steps20 → 1ы → щ3
387 max steps100 → 0ьь → ыь1 → ъь2 → щь3 → шь4 → чь5 → ць6 → хь7 → фь8 → уь9 → тьA → сьB → рьC → пьD → оьE → ньF → мьG → льH → кьI → йьJ → иьK → зьL → жьM → еьN → дьO → гьP → вьQ → бьR → аьS → ЯьT → ЮьU → ЭьV → ЬьW → ЫьX → ЪьY → ЩьZ → Шьa → Чьb → Цьc → Хьd → Фьe → Уьf → Тьg → Сьh → Рьi → Пьj → Оьk → Ньl → Мьm → Льn → Кьo → Йьp → Иьq → Зьr → Жьs → Еьt → Дьu → Гьv → Вьw → Бьx → Аьy → ωьz → ψьΑ → χьΒ → φьΓ → υьΔ → τьΕ → σьΖ → ςьΗ → ρьΘ → πьΙ → οьΚ → ξьΛ → νьΜ → μьΝ → λьΞ → κьΟ → ιьΠ → θьΡ → ηьΣ → ζьΤ → εьΥ → δьΦ → γьΧ → βьΨ → αьΩ → Ωьα
410 max stepsG00R → RFмв → ЭЖrW → χΒφΓ → jgСР → αΥδα → 7ььх → х6х8 → пмFE → бЬVS → ЕφΒu
565 max steps10006 → 60ьыч → ьфь71 → ыфь72 → ъуь83 → щсьA4 → шоьD5 → чкьH6 → цеьM7 → хЯьS8 → фШьZ9 → уРьhA → тЗьqB → сχьΑC → рμьΜD → пΩьΩE → оΛьνF → нΨьαG → мΚьξH → лΧьβI → кΙьοJ → йΦьγK → иΘьπL → зΥьδM → жΗьρN → еΤьεO → дΖьςP → гΣьζQ → вΕьσR → бΡьηS → аΔьτT → ЯΠьθU → ЮΓьυV → ЭΟьιW → ЬΒьφX → ЫΞьκY → ЪΑьχZ → ЩΝьλa → Шzьψb → ЧΜьμc → Цyьωd → ХΛьνe → ФxьАf → УΚьξg → ТwьБh → СΙьοi → РvьВj → ПΘьπk → ОuьГl → НΗьρm → МtьДn → ЛΖьςo → КsьЕp → ЙΕьσq → ИrьЖr → ЗΔьτs → ЖqьЗt → ИΑьχr → ЗuьГs → Жzьψt → ЕtьДu → ЕxьАu → ДuьГv → ДvьВv → ГvьВw → ГtьДw