Base 130: 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 65 nodes0Т → С1 → П3 → Л7 → ГF → νV → ΕΒ → 2Р → Н5 → ЗB → υN → Φl → Yκ → yΘ → 8К → БH → ιZ → wΚ → CЖ → σP → Ρp → Qς → Οr → Mφ → Ψj → cζ → qΠ → Oτ → Τn → Uξ → Ηz → 6М → ЕD → ρR → Νt → IА → ηb → sΞ → Kψ → γf → kΧ → aθ → uΜ → GВ → λX → ΑΖ → 4О → Й9 → ωJ → εd → oΣ → Sπ → Λv → EД → οT → Ιx → AИ → χL → αh → gβ → iΩ → eδ → mΥ → Wμ → ΓΔ
31 cycle (fixed) 1 node ΓТΔ
486 cycles6 nodesI5МБ → ЗθZC → υvΚO → ΦDДm → ρXκS → ΝzΖu
53 cycles4 nodesαgТαi → βfТβh → γhТΩg → βiТΨh
616 cycles50 nodesYT1Рολ → ПΚzΖw4 → ЛD5МЕ8 → ЗГρQFC → υξΞrUO → ΦΘLφym → αY8Йκi → БzfβΗI → ιk6ЛΧa → ЕwaηΚE → ρuCЕΜS → σΝGБtQ → λΡIωpY → ηΑQρΖc → Οs4НΞs → ЙMKχφA → ωγΨifK → εldδΦe → pnYιΤΣ → yVRπνΙ → ΝΖ9ИΑu → ωI4НАK → ЙθδdaA → ωvnΣΛK → εUEГξe → οΘnΣyU → ΙU8Йξy → БΘ9ИyI → ωι8ЙZK → БεwΙdI → ιpBЖΡa → υwQρΚO → ΦΟCЕrm → σYMυκQ → ΨΡyΗpk → cR7Кρη → ГΞrΞsG → νMKχφW → γΩΔΒig → kf1РγΨ → ПlbζΦ4 → ЛsYιΞ8 → ГyKχΘG → νγ8ЙfW → БΕkΦΒI → ιa2Пθa → НwuΛΚ6 → ЗGCЕВC → υσλWPO → ΦΣΒΔom