Base 163: 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
214 max steps10 → 0у → т1 → р3 → м7 → дF → ФV → ξΒ → ZР → ζΚ → Jа → Мd → ΧΣ → 3р → м7
384 max steps100 → 0уу → ту1 → су2 → ру3 → пу4 → оу5 → ну6 → му7 → лу8 → ку9 → йуA → иуB → зуC → жуD → еуE → дуF → гуG → вуH → буI → ауJ → ЯуK → ЮуL → ЭуM → ЬуN → ЫуO → ЪуP → ЩуQ → ШуR → ЧуS → ЦуT → ХуU → ФуV → УуW → ТуX → СуY → РуZ → Пуa → Оуb → Нуc → Муd → Луe → Куf → Йуg → Иуh → Зуi → Жуj → Еуk → Дуl → Гуm → Вуn → Буo → Ауp → ωуq → ψуr → χуs → φуt → υуu → τуv → σуw → ςуx → ρуy → πуz → οуΑ → ξуΒ → νуΓ → μуΔ → λуΕ → κуΖ → ιуΗ → θуΘ → ηуΙ → ζуΚ → εуΛ → δуΜ → γуΝ → βуΞ → αуΟ → ΩуΠ → ΨуΡ → ΧуΣ → ΦуΤ → ΥуΥ → ΤуΦ → ΥуΥ
485 max stepsΦ000 → ΥууΥ → ΥΤΥΦ → 1уут → т0т2 → тп32 → рл74 → мгF8 → дУVG → ФνΒW → ξYРΓ → θYРΙ → θMЬΙ → ЖMЬk → ЖΙζk → ΚKЮη → КKЮg → КΡΧg → Σ4оΨ → к4оA → кЯJA → аЛdK → МΦΣe → Χ2рΤ → о2р6 → озB6 → иЫNC → ЬГlO → ДΕκm → ΖSЦλ → τSЦw → τkДw → ΘkДι → ΘOЪι → ВOЪo → ВΑξo → ΒaОο → δaОΝ → δEдΝ → ЦEдU → ЦρxU → ςgИy → ΠgИα → Π8кα → в8кI → вПZI → РεΚa → ζIаΛ → ОIаc → ОαΞc → βAиΟ → ЮAиM → ЮЗhM → ИΝβi → ΞCжγ → ЪCжQ → ЪωpQ → Аwςq → xiЖσ → ΜiЖε → ΜGвε → ТGвY → ТιΖY → κQШΗ → ψQШs → ψsφs → tqψχ → vqψυ → vmВυ → ΔmВν → ΔWТν → μWТΕ → μUФΕ → πUФΑ → πcМΑ → ΩcМΡ → Ω6мΡ → ж6мE → жЧRE → ШυtS → φoАu → zoАρ → zeКρ → ΥeКΦ → Υ0тΦ → т0т2
566 max steps10000 → 0уууу → тууу1 → т0ут2 → упу31 → тпу32 → соу43 → рму64 → пйу95 → оеуD6 → науI7 → мЪуO8 → лУуV9 → кЛуdA → йВуmB → иςуwC → зηуΘD → жΤуΥE → еΗуθF → дΣуΦG → гΖуιH → вΡуΧI → бΕуκJ → аΠуΨK → ЯΔуλL → ЮΟуΩM → ЭΓуμN → ЬΞуαO → ЫΒуνP → ЪΝуβQ → ЩΑуξR → ШΜуγS → ЧzуοT → ЦΛуδU → ХyуπV → ФΚуεW → УxуρX → ТΙуζY → СwуςZ → РΘуηa → Пvуσb → ОΗуθc → Нuуτd → МΖуιe → Лtуυf → КΕуκg → Йsуφh → ИΔуλi → Зrуχj → ЖΓуμk → Еqуψl → ДΒуνm → Гpуωn → ВΑуξo → БoуАp → Бyуπp → Аpуωq → Аwуςq → ωqуψr → ωuуτr → ψrуχs → ψsуφs → χsуφt → χqуψt → ωrуχr → ψuуτs → χqуψt