Base 156: 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

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 steps100
228 max steps20 → 1л → й3е7ЭFНVηΒνvΝΥЯDСRοtΕδωjΓζρrΡΠл1й3
380 max steps100 → 0мм → лм1 → км2 → йм3 → им4 → зм5 → жм6 → ем7 → дм8 → гм9 → вмA → бмB → амC → ЯмD → ЮмE → ЭмF → ЬмG → ЫмH → ЪмI → ЩмJ → ШмK → ЧмL → ЦмM → ХмN → ФмO → УмP → ТмQ → СмR → РмS → ПмT → ОмU → НмV → МмW → ЛмX → КмY → ЙмZ → Имa → Змb → Жмc → Емd → Дмe → Гмf → Вмg → Бмh → Амi → ωмj → ψмk → χмl → φмm → υмn → τмo → σмp → ςмq → ρмr → πмs → οмt → ξмu → νмv → μмw → λмx → κмy → ιмz → θмΑ → ηмΒ → ζмΓ → εмΔ → δмΕ → γмΖ → βмΗ → αмΘ → ΩмΙ → ΨмΚ → ΧмΛ → ΦмΜ → ΥмΝ → ΤмΞ → ΣмΟ → ΡмΠ → ΠмΡΠмΡ
422 max steps500Y → Y4зЛ → гβΖA → ЩJШK → ЖГed → ΡΜΥΡ → 7мме → е6е8 → ЯЬFE → СМVS → οζΒuiRРБοΖβuiJШБЕΖβeΟJШΤЕ3иeеΞΣ8Э3иGеМV8ЭζΒGНRРWοζΒu
562 max steps10009 → 90млд → мбмA1 → лбмA2 → камB3 → йЮмD4 → иЫмG5 → зЧмK6 → жТмP7 → еМмV8 → дЕмc9 → гχмkA → вξмtB → бδмΔC → аΡмΟD → ЯΕмγE → ЮΞмΣF → ЭΔмδG → ЬΝмΤH → ЫΓмεI → ЪΜмΥJ → ЩΒмζK → ШΛмΦL → ЧΑмηM → ЦΚмΧN → ХzмθO → ФΙмΨP → УyмιQ → ТΘмΩR → СxмκS → РΗмαT → ПwмλU → ОΖмβV → НvмμW → МΕмγX → ЛuмνY → КΔмδZ → Йtмξa → ИΓмεb → Зsмοc → ЖΒмζd → Еrмπe → ДΑмηf → Гqмρg → Вzмθh → Бpмςi → Аyмιj → ωoмσk → ψxмκl → χnмτm → φwмλn → υmмυo → φtмξn → υpмςo → τsмοp → σoмσq → τpмςp → σrмπq → ςoмσr → τoмσp → τrмπp → σpмςqσpмςq