Base 176: 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

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
231 max steps20 → 1я → э3щ7сFбVБΒΡμЫbοΞПnΟξУjΨζуDеRЙtΓАΦθлLХhγβ0ァя1э3
390 max steps100 → 0ァァ → яァ1 → юァ2 → эァ3 → ьァ4 → ыァ5 → ъァ6 → щァ7 → шァ8 → чァ9 → цァA → хァB → фァC → уァD → тァE → сァF → рァG → пァH → оァI → нァJ → мァK → лァL → кァM → йァN → иァO → зァP → жァQ → еァR → дァS → гァT → вァU → бァV → аァW → ЯァX → ЮァY → ЭァZ → Ьァa → Ыァb → Ъァc → Щァd → Шァe → Чァf → Цァg → Хァh → Фァi → Уァj → Тァk → Сァl → Рァm → Пァn → Оァo → Нァp → Мァq → Лァr → Кァs → Йァt → Иァu → Зァv → Жァw → Еァx → Дァy → Гァz → ВァΑ → БァΒ → АァΓ → ωァΔ → ψァΕ → χァΖ → φァΗ → υァΘ → τァΙ → σァΚ → ςァΛ → ρァΜ → πァΝ → οァΞ → ξァΟ → νァΠ → μァΡ → λァΣ → κァΤ → ιァΥ → θァΦ → ηァΧ → ζァΨ → εァΩ → δァα → γァβ → βァγβァγ
421 max steps100A → A0яч → ямJ2 → эШd4 → щκΣ8 → сFрG → вЯWV → ГψΔΑ → qhФН → γΚςγ → Vァァб → бUбW → ГАΒΑ → qlРН → ΤΚςλ → WFрб → бАΒWБlРΓΤlРλΤFрλбFрWбАΒW
569 max stepsβ0000 → αァァァδ → δΩァδβ → ε1ァюα → яαァγ2 → юβァβ3 → эΩァδ4 → ьαァγ5 → ыΨァε6 → ъΩァδ7 → щΧァζ8 → шΨァε9 → чΦァηA → цΧァζB → хΥァθC → фΦァηD → уΤァιE → тΥァθF → сΣァκG → рΤァιH → пΡァλI → оΣァκJ → нΠァμK → мΡァλL → лΟァνM → кΠァμN → йΞァξO → иΟァνP → зΝァοQ → жΞァξR → еΜァπS → дΝァοT → гΛァρU → вΜァπV → бΚァςW → аΛァρX → ЯΙァσY → ЮΚァςZ → ЭΘァτa → ЬΙァσb → ЫΗァυc → ЪΘァτd → ЩΖァφe → ШΗァυf → ЧΕァχg → ЦΖァφh → ХΔァψi → ФΕァχj → УΓァωk → ТΔァψl → СΒァАm → РΓァωn → ПΑァБo → ОΒァАp → НzァВq → МΑァБr → ЛyァГs → КzァВt → ЙxァДu → ИyァГv → ЗwァЕw → ЖxァДx → ЕvァЖy → ЗuァЗw → ИxァДv → ЗxァДwЖwァЕxЖvァЖxЗvァЖwЗxァДw