Base 120: 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

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 cycles55 nodes0И → З1 → Е3 → Б7 → σF → γV → uΒ → 6В → υD → ηR → Γt → 8А → ρH → ΨZ → mΚ → Mμ → Νj → Sζ → Αv → 4Д → ω9 → οJ → Τd → eΣ → cΥ → gΠ → YΩ → oΘ → Iπ → Φb → iΞ → Uδ → wz → 2Ж → Г5 → χB → λN → Λl → Oκ → Ιn → Kξ → Ρf → aΧ → kΜ → Qθ → Εr → Cφ → ιP → Ηp → Gς → αX → qΖ → Eτ → εT → yx
31 cycle (fixed) 1 node xИy
47 cycles4 nodese7АΤ → σdΣG → γdΣW → udΣΓ
52 cycles2 nodesywИyy → yИИИx
66 cycles61 nodescV7АγΦ → σvhΞΑG → γW4ГβW → ωusΓΒA → οA6БψK → υξΣdKE → ηΣdΣeS → ΓecΤΣu → gd7АΤΡ → σfZΧΡG → γmaΦΚW → ukMλΜΓ → ΝR7Аηk → σΔRζsG → γΓAχtW → νu8ωΒM → ρΟ6БhI → υΨWαZE → ηsmΙΔS → ΓMAχμu → νΞ7АiM → σΟUγhG → γwWαzW → us2ЕΔΓ → ГB7Аχ6 → χσλMFC → λδΜjUO → ΛxRζym → ΓO0Зκu → ЗΚ7Аm2 → ЕσMλF4 → БδΜjU8 → σxRζyG → γΓ0ЗtW → Зu8ωΒ2 → Еρ6БH4 → БυΨYD8 → σθnΘQG → γΖJξqW → ΤuEσΒe → εe6БΣU → υycΤxE → ηg0ЗΠS → ЗΓYΨt2 → Еo8ωΘ4 → БρIοH8 → σΩΥbYG → γphΞΗW → uWGρβΓ → αt7АΓY → σq8ωΖG → ργEσVI → εΨuΑZU → yn5ВΙy → χKИИνC → φξ9ψKD → οιΡePK → ΤΘbΥoe → ieIοΣΟ → ΦdVβΤc → uieΡΞΓ