Base 138: 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

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
271 max steps20 → 1Щ → Ч3У7ЛFυVΝΒЕLιhΓΜЙHρZΕΚС9ЗJνdλfΤvηjγnσXΙΖХ5ПBГNεlΛΔНDωRΦtΨrΟzχTΡxοbΑΞБPαpΗΘЩ1Ч3
371 max steps100 → 0ЪЪ → ЩЪ1 → ШЪ2 → ЧЪ3 → ЦЪ4 → ХЪ5 → ФЪ6 → УЪ7 → ТЪ8 → СЪ9 → РЪA → ПЪB → ОЪC → НЪD → МЪE → ЛЪF → КЪG → ЙЪH → ИЪI → ЗЪJ → ЖЪK → ЕЪL → ДЪM → ГЪN → ВЪO → БЪP → АЪQ → ωЪR → ψЪS → χЪT → φЪU → υЪV → τЪW → σЪX → ςЪY → ρЪZ → πЪa → οЪb → ξЪc → νЪd → μЪe → λЪf → κЪg → ιЪh → θЪi → ηЪj → ζЪk → εЪl → δЪm → γЪn → βЪo → αЪp → ΩЪq → ΨЪr → ΧЪs → ΦЪt → ΥЪu → ΤЪv → ΣЪw → ΡЪx → ΠЪy → ΟЪz → ΞЪΑ → ΝЪΒ → ΜЪΓ → ΛЪΔ → ΚЪΕ → ΙЪΖ → ΘЪΗ → ΗЪΘΗЪΘ
429 max stepsH00q → qGЙα → σXςY → ΚΗΗΖ → 3ЪЪЧ → Ч2Ч4 → ХТ76 → ПКFCГτVOεΜΒmg9РλЗrΧKνTφeΡvΣyMHИЕρθhaΕnβΛc5ФοПzΞCГDМOωδlSΦfκusPАΨαTφqΡXςyΙHИΗρ1ШaЧΔΚ4У5Ф8ПКFC
558 max steps10000 → 0ЪЪЪЪ → ЩЪЪЪ1 → Щ0ЪЩ2 → ЪЦЪ31 → ЩЦЪ32 → ШХЪ43 → ЧУЪ64 → ЦРЪ95 → ХМЪD6 → ФЗЪI7 → УБЪO8 → ТτЪV9 → СμЪdA → РγЪmB → ПΡЪwC → ОΖЪΘD → НvЪΣE → МΕЪΙF → ЛuЪΤG → КΔЪΚH → ЙtЪΥI → ИΓЪΛJ → ЗsЪΦK → ЖΒЪΜL → ЕrЪΧM → ДΑЪΝN → ГqЪΨO → ВzЪΞP → БpЪΩQ → АyЪΟR → ωoЪαS → ψxЪΠT → χnЪβU → φwЪΡV → υmЪγW → τvЪΣX → σlЪδY → ςuЪΤZ → ρkЪεa → πtЪΥb → οjЪζc → ξsЪΦd → νiЪηe → μrЪΧf → λhЪθg → κqЪΨh → ιgЪιi → κnЪβh → ιjЪζi → θmЪγj → ηiЪηk → θjЪζj → ηlЪδk → ζiЪηl → θiЪηj → θlЪδj → ηjЪζkηjЪζk