Base 154: 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
бвгдежзийклмнопр

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--
27 cycles20 nodes8в → ЩH → ЗZ → ΦΚ → Aа → ХL → ωh → Εβ → KЦ → Бf → ΙΧ → CЮ → СP → ρp → oς → qπ → mτ → uμ → eВ → ΛΥ
31 cycle (fixed) 1 node ΟкΠ
427 cycles30 nodesQ1иС → зπp4 → гnς8 → ЫrξG → ЛjφW → εzζΓ → UPРН → ρθxq → oXИσ → αrξΗ → kHШχ → Зzζa → ΦTМΛ → ι9аy → ЧXИK → ГΩΖe → ΝHШΤ → З5дa → ЯΥΚC → У9аO → ЧτlK → Гvκe → ΝbДΤ → Ρ5дΟ → Я1иC → зТN4 → гτl8 → ЫvκG → ЛbДW → εΠΞΓ
53 cycles4 nodesρoкρq → ςnкςp → σpкπo → ςqкοp