Base 139: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
24 max steps10 → 0Ы → Ъ1 → Ш3 → Ф7
370 max steps100 → 0ЫЫ → ЪЫ1 → ЩЫ2 → ШЫ3 → ЧЫ4 → ЦЫ5 → ХЫ6 → ФЫ7 → УЫ8 → ТЫ9 → СЫA → РЫB → ПЫC → ОЫD → НЫE → МЫF → ЛЫG → КЫH → ЙЫI → ИЫJ → ЗЫK → ЖЫL → ЕЫM → ДЫN → ГЫO → ВЫP → БЫQ → АЫR → ωЫS → ψЫT → χЫU → φЫV → υЫW → τЫX → σЫY → ςЫZ → ρЫa → πЫb → οЫc → ξЫd → νЫe → μЫf → λЫg → κЫh → ιЫi → θЫj → ηЫk → ζЫl → εЫm → δЫn → γЫo → βЫp → αЫq → ΩЫr → ΨЫs → ΧЫt → ΦЫu → ΥЫv → ΤЫw → ΣЫx → ΡЫy → ΠЫz → ΟЫΑ → ΞЫΒ → ΝЫΓ → ΜЫΔ → ΛЫΕ → ΚЫΖ → ΙЫΗ → ΘЫΘ
44 max stepsΙ000 → ΘЫЫΘ → ΘΗΘΙ → 1ЫЫЪ → Ъ0Ъ2
553 max steps1000C → C0ЫЪР → ЫНЫD1 → ЪНЫD2 → ЩМЫE3 → ШКЫG4 → ЧЗЫJ5 → ЦГЫN6 → ХψЫS7 → ФςЫY8 → УλЫf9 → ТγЫnA → СΣЫwB → РΘЫΗC → ПwЫΣD → ОΖЫΙE → НvЫΤF → МΕЫΚG → ЛuЫΥH → КΔЫΛI → ЙtЫΦJ → ИΓЫΜK → ЗsЫΧL → ЖΒЫΝM → ЕrЫΨN → ДΑЫΞO → ГqЫΩP → ВzЫΟQ → БpЫαR → АyЫΠS → ωoЫβT → ψxЫΡU → χnЫγV → φwЫΣW → υmЫδX → τvЫΤY → σlЫεZ → ςuЫΥa → ρkЫζb → πtЫΦc → οjЫηd → ξsЫΧe → νiЫθf → μrЫΨg → λhЫιh → κqЫΩi → ιgЫκj → λnЫγh → κkЫζi → ιmЫδj → θjЫηk → θkЫζk → ηkЫζl → ηiЫθl