Base 100: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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 50 nodes0ξ → ν1 → λ3 → η7 → ΨF → ΗV → aΒ → QΜ → kr → 6θ → αD → ΛR → it → Aδ → ΡL → uh → Cβ → ΝP → mp → 2μ → ι5 → γB → ΟN → ql → 4κ → ε9 → ΤJ → yd → KΣ → wf → GΧ → ΕX → WΖ → YΔ → UΘ → cz → MΠ → sj → 8ζ → ΦH → ΓZ → SΚ → gv → EΩ → ΙT → ex → IΥ → Αb → OΞ → on
31 cycle (fixed) 1 node nξo
48 cycles10 nodesa3κΓ → ηRΚ8 → ΨhtG → ΗBβW → ΟZΒO → qRΚm → i3κu → ηBβ8 → ΨΞNG → ΗplW
53 cycles4 nodesΕWξΕY → ΖVξΖX → ΗXξΔW → ΖYξΓX
67 cycles196 nodesKGCαΧΤ → ΝΖxdWQ → mZJΣΓq → yT3κΙe → ηfJΣw8 → ΨyGΦdG → ΗΕKΡXW → waWΕΒg → YRFΧΛΕ → ΗjVΖsW → bZ8εΓΒ → ΦTPΜΙI → Γmewpa → SI2λΥΛ → ιΒhta6 → γRBβΛC → ΠΞisON → sp9δmk → Τ82λζK → ιΧxdG6 → γΖJΣWC → ΟyYΓdO → qUKΡΘm → wd3κyg → ηLFΧΡ8 → ΨΗugVG → ΗbDΩΑW → ΛaOΝΒS → oiQΛto → kAξξγs → δrXΔkB → ΡW6ηΖM → αuYΓhE → ΛUCαΘS → ΝicytQ → mMAγΠq → Ρt3κiM → ηuAγh8 → ΨΡCαLG → ΝΗugVQ → mbDΩΑq → ΛP3κΝS → ηnhto8 → ΨC0νβG → νΞΖVO2 → λpZΒm4 → ηS2λΚ8 → ιΨguF6 → γΘDΩUC → ΟΛcyRO → qjLΠsm → u93κεi → ηΥBβI8 → ΨΟΑaNG → ΗrPΜkW → ma6ηΒq → αR3κΛE → ηΛisR8 → Ψj9δsG → ΤΗ8εVK → ΦyaΑdI → ΓQKΡΜa → wlRΚqg → iG4ιΧu → εΖBβWA → ΤΟYΓNK → yrTΘke → eK6ηΣy → αxJΣeE → ΛyIΤdS → ΑiKΡtc → wOAγΞg → ΡpFΧmM → Ηu2λhW → ιaCαΒ6 → γΝQΛPC → ΟnjroO → q80νζm → νΧ3κG2 → ληΕW74 → ηΩXΔE8 → ΨΚVΖSG → ΗhZΒuW → aSCαΚΓ → ΝhRΚuQ → miCαtq → ΝB3κγQ → ηΠlpM8 → Ψt3κiG → ηΗAγV8 → ΨΡaΑLG → ΗvPΜgW → maEΨΒq → ΙR3κΛU → ηjdxs8 → ΨK8εΣG → ΦΗweVI → ΓbHΥΑa → ΓSOΝΚa → ohRΚuo → iCξξαu → βtTΘiD → ΝeAγxQ → ΡmIΤpM → Αu2λhc → ιOCαΞ6 → γΝomPC → Οn1μoO → λq0νl4 → νη4ι72 → λεΨE94 → ηΥΘTI8 → ΨΒdxaG → ΗRJΣΛW → yjZΒse → SK8εΣΛ → ΦxhteI → ΓJBβΤa → ΟzRΚcO → qiMΟtm → sB3κγk → ηΠ7ζM8 → ΩΧsiGF → ΙΖ9δWU → ΤeYΓxK → yUIΤΘe → ΑdJΣyc → yOKΡΞe → wpJΣmg → yG2λΧe → ιΖJΣW6 → γyYΓdC → ΟUKΡΘO → wqcylg → MG4ιΧΡ → εΖthWA → ΤZBβΓK → ΟySΙdO → qgKΡvm → wF3κΨg → ηΘFΧU8 → ΨΗcyVG → ΗbLΠΑW → uaOΝΒi → oRBβΛo → ΟiξξsO → ΞtLΠiP → uoAγni → ΡC0νβM → νΞthO2 → λpBβm4 → ηΟ2λN8 → ιΨqkF6 → γΘ5θUC → γΟcyNC → ΟrLΠkO → uq6ηli → αC4ιβE → εΞΚROA → ΤphtmK → yC2λβe → ιΞJΣO6 → γyomdC → ΟL1μΡO → λvplg4 → ηF3κΨ8 → ηΨΗUF8 → ΨΘbzUG → ΗdNΞyW → qaKΡΒm → wR3κΛg → ηjFΧs8 → ΨΗ8εVG → ΦΗaΑVI → ΓbPΜΑa → mSOΝΚq → oh3κuo → ηCξξα8 → ζβ5θC9 → γΦΝOHC → ΟΔnnYO → qUξξΗm → ΘpFΧmV → Ηc2λzW → ιaMΟΒ6 → γsQΛjC → Οk8εrO → Φq6ηlI → αΓ4ιZE → εΛSΙRA → ΤjfvsK → yG8εΧe → ΦΖJΣWI → ΓyYΓda → USKΡΚΙ → whdxug
72 cycles19 nodesΝmNξΞpQ → ΟnPξΜoO → ΞpNξΞmP → ΟoQξΛnO → ΞoMξΟnP → ΠpPξΜmN → ΟqOξΝlO → ΞqQξΛlP → ΝnOξΝoQ → ΞmOξΝpP → ΞoPξΜnP → ΝoNξΞnQ → ΟnOξΝoO → ΞqOξΝlP → ΞoQξΛnP → ΝnMξΟoQ → ΠoOξΝnN → ΟrOξΝkO → ΞqRξΚlP