Base 141: 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
23 max steps10 → 0Э → Ь1 → Ъ3
371 max steps100 → 0ЭЭ → ЬЭ1 → ЫЭ2 → ЪЭ3 → ЩЭ4 → ШЭ5 → ЧЭ6 → ЦЭ7 → ХЭ8 → ФЭ9 → УЭA → ТЭB → СЭC → РЭD → ПЭE → ОЭF → НЭG → МЭH → ЛЭI → КЭJ → ЙЭK → ИЭL → ЗЭM → ЖЭN → ЕЭO → ДЭP → ГЭQ → ВЭR → БЭS → АЭT → ωЭU → ψЭV → χЭW → φЭX → υЭY → τЭZ → σЭa → ςЭb → ρЭc → πЭd → οЭe → ξЭf → νЭg → μЭh → λЭi → κЭj → ιЭk → θЭl → ηЭm → ζЭn → εЭo → δЭp → γЭq → βЭr → αЭs → ΩЭt → ΨЭu → ΧЭv → ΦЭw → ΥЭx → ΤЭy → ΣЭz → ΡЭΑ → ΠЭΒ → ΟЭΓ → ΞЭΔ → ΝЭΕ → ΜЭΖ → ΛЭΗ → ΚЭΘ → ΙЭΙ
44 max stepsΚ000 → ΙЭЭΙ → ΙΘΙΚ → 1ЭЭЬ → Ь0Ь2
556 max steps1000D → D0ЭЬС → ЭОЭE1 → ЬОЭE2 → ЫНЭF3 → ЪЛЭH4 → ЩИЭK5 → ШДЭO6 → ЧωЭT7 → ЦσЭZ8 → ХμЭg9 → ФδЭoA → УΤЭxB → ТΙЭΘC → СxЭΤD → РΗЭΚE → ПwЭΥF → ОΖЭΛG → НvЭΦH → МΕЭΜI → ЛuЭΧJ → КΔЭΝK → ЙtЭΨL → ИΓЭΞM → ЗsЭΩN → ЖΒЭΟO → ЕrЭαP → ДΑЭΠQ → ГqЭβR → ВzЭΡS → БpЭγT → АyЭΣU → ωoЭδV → ψxЭΤW → χnЭεX → φwЭΥY → υmЭζZ → τvЭΦa → σlЭηb → ςuЭΧc → ρkЭθd → πtЭΨe → οjЭιf → ξsЭΩg → νiЭκh → μrЭαi → λhЭλj → μoЭδi → λkЭθj → κnЭεk → ιjЭιl → κkЭθk → ιmЭζl → θjЭιm → κjЭιk → κmЭζk → ιkЭθl