Base 139: 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--
23 cycles12 nodes3Ш → Ф7 → МF → φV → ΞΒ → BР → ДN → ζl → hκ → pβ → Zς → ΖΚ
31 cycle 2 nodesΗЫΙ → ΘЫΘ
434 cycles69 nodesJAРЙ → ЖοbM → κΑΞi → pCОγ → ВaπQ → βΓΜq → Z8Тσ → КΗΘI → ς0Ъa → ЪΕΚ2 → Ш4Ц4 → ФС98 → МЗJG → φνdW → ΞwΣΓ → LAРЗ → ЖλfM → κsΧi → pSψγ → Υaπw → ΔMДΝ → θ8Тk → КkζI → ςiθa → ΖmδΛ → f4Цν → ТuΥA → ИOВK → ξγne → xcξΤ → zKЖΡ → μGКg → τsΧY → ΚSψΗ → Υ2Шw → ЦMД6 → РηjC → ДkζO → ζiθm → ngκε → reμα → vWτΦ → ΜOВΕ → δ6Фo → ОcξE → АyΠS → ΧGКu → τQАY → ΩΙΖs → V2Шχ → ЦΟz6 → РEМC → ДχTO → ζΡxm → hIИλ → πqΩc → ΒWτΟ → ΜCОΕ → В6ФQ → ОαpE → АYςS → ΧΗΘu → R0ЪБ → ЪΨr2 → ШUφ4 → ФΟz8 → МEМG → ψυVU → ΣΝΒy
52 cycles4 nodesηjЫηl → θiЫθk → ιkЫζj → θlЫεk