Base 135: Cycles Sequences: Maximum Length Cycle Count

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 # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
22 cycles4 nodesNА → βl → dκ → tΣ
31 cycle 2 nodesΕЧΗ → ΖЧΖ
489 cycles36 nodesJ0ЦЕ → Цλb2 → ФwΞ4 → РGЖ8 → ИοXG → ςΕΖW → Κ0ЦΓ → Ц6Р2 → ФЙD4 → РυR8 → ИΡtG → ςMАW → δΙΒk → h6Рη → КmΩE → φaμS → ΣyΜu → NCКБ → ψγjQ → Χgζq → nUςα → ΜaμΑ → zAМΝ → ВCКM → ψεhQ → Χkβq → fUςι → ΜqΥΑ → TAМυ → ВΟvM → ζIДi → μkβc → xeθΟ → rGЖΦ → πSτY → ΠΕΖw
51 cycle (fixed) 1 node εiЧδj
65 cycles157 nodesF91ХОЙ → ФЕσTI4 → РνΝxa8 → ИΑEИΛG → τς9НVU → ДΞΚΑxK → κG8ОЗe → ЖρsΣWI → ξΙOψΓa → ΩΒ5СΚo → МZ7ПξC → ИАΒΙNG → ςγ6РkW → КΚfηΒE → φp7ПΧS → ИΣVρtG → ςΚNωΒW → βΚ7ПΒm → Иd7ПκG → ИςtΡVG → ςΛMАΑW → δΚ9НΒk → Дh7ПζK → ИκlαdG → ςucκΡW → ΚvLБΠΓ → ζK6РГi → КιkβeE → φseθΤS → ΣrPχΥu → ΧSMАυq → δΡUςuk → ΜhLБζΑ → ζmAМαi → ВlbλβM → ζxdιΞi → tlFЗβΤ → ςeOψιW → ΩΚrΤΒo → ZR7Пφο → ИΤΓΘsG → ςQ4ТχW → ОΦΙΒqA → ДU6РσK → КκΜydE → φuCКΡS → ψΣLБtQ → ζΧNωpi → βlVρβm → ΚecκιΓ → vs6РΤΡ → КQKВχE → φθΥqfS → ΣqSτΦu → ΠUMАσw → δΝIДyk → μhDЙζc → φxlαΞS → ΣdFЗκu → ςuMАΡW → δΚLБΒk → ζh7Пζi → ИmkβαG → ςfbλθW → ΚxpΦΞΓ → VG6РЗσ → КρΛzWE → φΙAМΓS → ВΣ5СtM → МζNωhC → АβlαlO → βecκιm → vscκΤΡ → vQKВχΡ → θΦKВqg → θpTσΧg → ΞpVρΧy → ΚWEИρΓ → τΙ6РΓU → КΞ5СxE → МφFЗRC → АςΣsVO → βΛOψΑm → Ωd9Нκo → ДuYξΡK → κΔLБΘe → ζt3УΣi → РlNωβ8 → ИβdιlG → ςtdιΣW → ΚtNωΣΓ → βO6Рωm → КαcκmE → φvbλΠS → ΣxJГΞu → κNFЗАe → ςγsΣkW → ΚgOψηΓ → Ωo6РΨo → КZXοξE → φΖΒΙΖS → Σ6ЧЧРu → СΡlαu7 → КdLБκE → φζtΡhS → ΣmMАαu → δcMАλk → δwgζΟk → nhHЕζα → ξmaμαa → ΒzbλΜΛ → xC8ОЛΟ → ЖωGЖOI → πξΩmZY → ΖΓaμΙΗ → z60ЦСΝ → ЦЛCКC2 → ФωχPO4 → РαΦpm8 → ИcUςλG → ςΜvΟzW → ΚJBЛДΓ → Аλ6РcO → КβvΟlE → φeIДιS → μΣrΤtc → xRNωφΟ → βΤGЖsm → πdPχκY → ΧΖtΡΖq → VMЧЧАσ → Бς6РVN → КδΚΑjE → φi8ОεS → ЖΣjγtI → ξhNωζa → βΒlαΚm → ec7Пλκ → ИwsΣΟG → ςPHЕψW → ξΨΙΒoa → ΒY6РοΛ → КΕ8ОΗE → Жφ1ХRI → ФξΣsZ4 → РΓOψΙ8 → ИΩ5СnG → МςZνVC → АΛΑΚΑO → βA8ОНm → ЖГcκKI → ξιuΠea → ΒsKВΤΛ → θQ8Оχg → ЖΦoΧqI → ξXTσπa → ΞΗΑΚΕy