Base 138: 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--
21 cycle 69 nodes0Ъ → Щ1 → Ч3 → У7 → ЛF → υV → ΝΒ → AР → ЕL → ιh → oβ → aπ → ΓΜ → 8Т → ЙH → ρZ → ΕΚ → 4Ц → С9 → ЗJ → νd → wΣ → KЖ → λf → sΧ → Sψ → Τv → MД → ηj → kζ → iθ → mδ → eμ → uΥ → OВ → γn → cξ → yΠ → GК → σX → ΙΖ → 2Ш → Х5 → ПB → ГN → εl → gκ → qΩ → Wτ → ΛΔ → 6Ф → НD → ωR → Φt → QА → Ψr → Uφ → Οz → EМ → χT → Ρx → IИ → οb → ΑΞ → CО → БP → αp → Yς → ΗΘ
31 cycle (fixed) 1 node ΗЪΘ
429 cycles22 nodesE9РН → ЗψRK → νΥte → wPАΤ → αLДq → ιXςi → ΙnβΗ → c1Шο → ЧzΞ4 → УDМ8 → ЛψRG → υΥtW → ΝPАΓ → α9Рq → ЗXςK → νΘΖe → w1ШΤ → ЧLД4 → Уθh8 → ЛnβG → υbξW → ΝzΞΓ
52 cycles2 nodesΘΖЪΘΘ → ΘЪЪЪΗ