Base 137: 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
225 max steps10 → 0Щ → Ш1 → Ц3Т7КFτVΜΒЖJμdθhψRΥtΩpΘΖЦ3
371 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 → ωЩQ → ψЩR → χЩS → φЩT → υЩU → τЩV → σЩW → ςЩX → ρЩY → πЩZ → οЩa → ξЩb → νЩc → μЩd → λЩe → κЩf → ιЩg → θЩh → ηЩi → ζЩj → εЩk → δЩl → γЩm → βЩn → αЩo → ΩЩp → ΨЩq → ΧЩr → ΦЩs → ΥЩt → ΤЩu → ΣЩv → ΡЩw → ΠЩx → ΟЩy → ΞЩz → ΝЩΑ → ΜЩΒ → ΛЩΓ → ΚЩΔ → ΙЩΕ → ΘЩΖ → ΗЩΗΖЩΘΗЩΗ
438 max stepsΘ000 → ΗЩЩΗ → ΗΖΗΘ → 1ЩЩШ → Ш0Ш2ШХ32ЦС74ТЙF8КσVGτΛΒWΜ8РΓИ8РIИοZIπΓΚaΔ6ТΛМ6ТEМχREψΤtSΥOАuβOАoβaξoΒaξΝΒAОΝДAОMДηhMθmβincμγxcμΡxIЖΡξIЖcξyΞczEКΟφEКUφΟxUΠGИyςGИYςΗΖYΘ0ШΗШ0Ш2
555 max steps10000 → 0ЩЩЩЩ → ШЩЩЩ1 → Ш0ЩШ2 → ЩХЩ31 → ШХЩ32 → ЧФЩ43 → ЦТЩ64 → ХПЩ95 → ФЛЩD6 → УЖЩI7 → ТАЩO8 → СσЩV9 → РλЩdA → ПβЩmB → ОΠЩwC → НΕЩΘD → МvЩΡE → ЛΔЩΙF → КuЩΣG → ЙΓЩΚH → ИtЩΤI → ЗΒЩΛJ → ЖsЩΥK → ЕΑЩΜL → ДrЩΦM → ГzЩΝN → ВqЩΧO → БyЩΞP → АpЩΨQ → ωxЩΟR → ψoЩΩS → χwЩΠT → φnЩαU → υvЩΡV → τmЩβW → σuЩΣX → ςlЩγY → ρtЩΤZ → πkЩδa → οsЩΥb → ξjЩεc → νrЩΦd → μiЩζe → λqЩΧf → κhЩηg → ιpЩΨh → θgЩθi → ιmЩβh → θjЩεi → ηlЩγj → ζiЩζkηiЩζjηkЩδjζjЩεkζiЩζk