Base 141: 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 35 nodes1Ь → Ъ3 → Ц7 → ОF → ψV → ΠΒ → DР → ВR → Ωt → TА → Υx → LИ → μh → rβ → Xφ → ΜΖ → 5Ш → ТB → ЖN → θl → jκ → nζ → fξ → vΧ → PД → δp → bς → ΔΞ → 9Ф → КJ → πd → zΣ → HМ → τZ → ΘΚ
31 cycle 2 nodesΘЭΚ → ΙЭΙ
459 cycles46 nodesJCРЛ → ДρbQ → δΓΞq → bAТσ → ИΕΜM → μ6Цi → РqβE → ВYτS → ΩΙΘu → T0ЬБ → ЬΦv2 → ЪOД4 → Цεn8 → ОeξG → ψwΥW → ΠMЖΓ → κCРk → ДmζQ → δgμq → taςα → ΖUψΝ → Σ6ЦΑ → РGМE → ВυXS → ΩΛΖu → T4ШБ → ФΦvA → КOДK → πεne → zeξΤ → xIКΦ → ςMЖc → κΓΞk → nAТη → ИgμM → μsΩi → rUψγ → ΣYτΑ → ΚGМΙ → φ0ЬY → ЬΛΖ2 → Ъ4Ш4 → ЦУ98 → ОЙJG → ψοdW → ΠyΣΓ
51 cycle (fixed) 1 node ιkЭθl