Base 169: 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

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
211 max steps10 → 0щ → ш1 → ц3 → т7 → кF → ЪV → τΒ → fР → ΩΧ → 1ш → ц3
387 max steps100 → 0щщ → шщ1 → чщ2 → цщ3 → хщ4 → фщ5 → ущ6 → тщ7 → сщ8 → рщ9 → пщA → ощB → нщC → мщD → лщE → кщF → йщG → ищH → зщI → жщJ → ещK → дщL → гщM → вщN → бщO → ащP → ЯщQ → ЮщR → ЭщS → ЬщT → ЫщU → ЪщV → ЩщW → ШщX → ЧщY → ЦщZ → Хщa → Фщb → Ущc → Тщd → Сщe → Рщf → Пщg → Ощh → Нщi → Мщj → Лщk → Кщl → Йщm → Ищn → Зщo → Жщp → Ещq → Дщr → Гщs → Вщt → Бщu → Ащv → ωщw → ψщx → χщy → φщz → υщΑ → τщΒ → σщΓ → ςщΔ → ρщΕ → πщΖ → οщΗ → ξщΘ → νщΙ → μщΚ → λщΛ → κщΜ → ιщΝ → θщΞ → ηщΟ → ζщΠ → εщΡ → δщΣ → γщΤ → βщΥ → αщΦ → ΩщΧ → ΨщΨ → ΧщΩ → ΨщΨ
482 max stepsΩ000 → ΨщщΨ → ΨΧΨΩ → 1щщш → ш0ш2 → шх32 → цс74 → тйF8 → кЩVG → ЪσΒW → τeРΓ → βeРΦ → β4фΦ → р4фA → реJA → жСdK → ТγΣe → δ8рΤ → и8рI → иХZI → ЦλΚa → μOаΛ → ИOаo → ИΗξo → ΘUЪο → φUЪΑ → φiМΑ → ΣiМε → ΣAоε → дAоM → дНhM → ОΤβi → Υ6тγ → м6тE → мЭRE → ЮБtS → ВuАu → vsВБ → xsВω → xoЖω → ΖoЖρ → ΖYЦρ → ξYЦΙ → ξSЬΙ → АSЬw → АqДw → ΒqДυ → ΒgОυ → ΧgОα → Χ2цα → ф2ц6 → фнB6 → обNC → вЙlO → КΛκm → ΜMвλ → МMвk → МΟζk → ΠEкη → ЬEкU → ЬχxU → ψmИy → ΚmИν → ΚQЮν → ДQЮs → Дyφs → zkКχ → ΞkКι → ΞIжι → ФIжc → ФηΞc → θGиΟ → ШGиY → ШοΖY → πWШΗ → ςWШΕ → ςaФΕ → κaФΝ → κKдΝ → РKдg → РΨΧg → Ω0шΨ → ш0ш2
566 max steps30000 → 2щщщч → ч1щч3 → шущ52 → чтщ63 → црщ84 → хнщB5 → фйщF6 → удщK7 → тЮщQ8 → сЧщX9 → рПщfA → пЖщoB → оφщyC → нλщΚD → мΨщΧE → лΚщλF → кΦщΩG → йΙщμH → иΥщαI → зΘщνJ → жΤщβK → еΗщξL → дΣщγM → гΖщοN → вΡщδO → бΕщπP → аΠщεQ → ЯΔщρR → ЮΟщζS → ЭΓщςT → ЬΞщηU → ЫΒщσV → ЪΝщθW → ЩΑщτX → ШΜщιY → ЧzщυZ → ЦΛщκa → Хyщφb → ФΚщλc → Уxщχd → ТΙщμe → Сwщψf → РΘщνg → Пvщωh → ОΗщξi → НuщАj → МΖщοk → ЛtщБl → КΕщπm → ЙsщВn → ИΔщρo → ЗrщГp → ЖΓщςq → ЕqщДr → ЕΑщτr → ДrщГs → Дyщφs → ГsщВt → Гwщψt → ВtщБu → ВuщАu → БuщАv → БsщВv → ГtщБt → Вwщψu → БsщВv