Base 114: 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--
23 cycles44 nodes0В → Б1 → ω3 → υ7 → νF → ΦV → oΒ → Cπ → γP → Αp → Aς → ηL → Ιh → Qβ → yr → 6φ → οD → αR → wt → 2А → χ5 → ρB → εN → Εl → Iκ → Οb → cΞ → aΠ → eΜ → WΥ → mΔ → Gμ → ΤX → kΖ → Kθ → Λf → UΧ → qz → 8τ → λH → ΡZ → gΚ → SΩ → uv
31 cycle (fixed) 1 node uВv
442 cycles9 nodesUHκΨ → Ρrxa → g5φΛ → ρTΧC → εrxO → Ε5φm → ρHκC → εΠZO → ΕfΚm
52 cycles2 nodesvtВvv → vВВВu
67 cycles127 nodesA64χφσ → σπθJCA → ιδΜdOK → ΝΔXΣme → kYGλΣΗ → ΤjLζΗY → ΙkMεΖi → ΗQKηβk → ΛzLζqg → ΙU8σΧi → λrPβyI → ΡΑ6υpa → οgAρΚE → ηαSΨRM → Ιxtvsi → Q51Аχγ → ωςzpA4 → υθ9ςK8 → νιΛeJG → ΦΞVΥcW → pnaΟΓΒ → eFBπνΝ → εΧXΣUO → ΕrjΖym → MI6υκη → οΠΘhaE → αfPβΛS → ΑwUΦtq → qA2ωςΑ → χθ9ςK6 → ριΛeJC → εΞVΥcO → ΕoaΟΒm → eICοκΝ → γΠXΣaQ → ΑkeΛΖq → WL9ςηΦ → ιΚnΒgK → ΝTDξΨe → αtXΣwS → wk2ωΖu → χL1Аη6 → ωρΙgB4 → υζRΩM8 → νΘvtiG → ΦP1АγW → ωΒnΒo4 → υECοξ8 → νγΨSPG → ΦΒtvoW → oD1АοΓ → ωβDξQ4 → υαyqR8 → νx7τsG → νΦ4χVG → σΦoΑVA → ιpBπΑK → εΝAρdO → ηΕYΡlM → ΙiIιΘi → ΟQOγβc → ΓzbΞqo → cE8σξΟ → λΩbΞSI → ΡvbΞua → gc0БΞΛ → БbTΧΟ2 → ωscΝx4 → υa4χΠ8 → σνeΛFA → ιΧVΥUK → ΝrnΒye → YE6υξΤ → οΩjΖSE → αvLζuS → Ιw0Бti → БQ2ωβ2 → ωχyq54 → υς7τA8 → ξμηKGF → ΨΥΚfWU → snTΧΓy → sF5φνy → ρΧ5φUC → ρεqyNC → εΖ7τkO → νΕKηlG → ΦΛIιfW → ΟoUΦΒc → qcCοΞΑ → γb9ςΟQ → ιΑcΝpK → ΝaAρΠe → ηfXΣΛM → ΙkUΦΖi → qQKηβΑ → Λz9ςqg → ιU8σΧK → λΝqydI → ΡZ7τΡa → νhfΚΙG → ΦUQαΧW → yrnΒys → E75φυο → ρξΩREC → εΩvtSO → Εv1Аum → ωI0Бκ4 → БυΟa72 → ωξdΜE4 → υΩXΣS8 → νvjΖuG → ΦM0БζW → БΘnΒi2 → ωPDξγ4 → υαΑoR8 → νxBπsG → εΦ4χVO → σΕoΑlA → ιJBπιK → εΞΜdcO → ΕbXΣΟm → kdHκΝΗ → ΡZLζΡa → ΙhfΚΙi → URPβαΨ → Αxrxsq