Base 109: 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--
23 cycles20 nodes1φ → τ3 → π7 → θF → ΠV → jΒ → Hζ → ΜZ → bΚ → XΞ → fΖ → PΧ → vp → 5ς → μB → ΩN → zl → Dκ → ΥR → rt
31 cycle 2 nodesrχt → sχs
481 cycles18 nodesJ6πε → κΙbE → ΥWΞS → rgΔu → N2τα → ςΑj6 → μGζC → ΩΝXO → zeΖm → RCκΦ → ΧsrQ → v0φq → φ4ς2 → τν94 → πγJ8 → θΗdG → ΠSΣW → piΒw
52 cycles4 nodesΛZχΛb → ΜYχΜa → ΝaχΚZ → ΜbχΙa
64 cycles176 nodesB53σςν → πναLA8 → θγΓhKG → ΠΗKβeW → ΖjRΤΒg → rPHεΧu → Μw2τoa → ςb7οΚ6 → μθXΝFC → ΩΡeΖUO → zmQΥym → tDBλκs → ΩΦ0φQO → φztql2 → τE2τι4 → ςπΣS76 → μιovEC → ΩΤ6πSO → κzpulE → ΥE4ςιS → ξΤqtSA → δq2τuK → ςΘ3σd6 → πμTΡB8 → θαmxMG → ΠΓAμiW → βjJγΒM → ΘΔHεhe → ΜTLαΣa → ΔoaΚwi → ZL7οβΝ → θΕcΘgG → ΠVNΨΠW → zkiΒΑm → JGCκηε → ΧΟΙbWQ → viWΞΓq → hK4ςγΕ → ξΗMΩeA → δΒRΤjK → ΘrHεte → ΜT1υΣa → τoaΚw4 → πZ7οΜ8 → ιηbΙGF → ΣΟWΞWU → nigΔΓy → NKAμγα → βΗΑjeM → ΔSGζΤi → ΞqKβuY → Ζf3σΖg → πQOΧΦ8 → θxtqnG → ΠA2τνW → ςγiΒK6 → μΗIδeC → ΩΚRΤbO → zrXΝtm → fD1υκΗ → τΦQΥQ4 → πusrq8 → θ40φσG → φοΟV82 → τηiΒG4 → πΟIδW8 → θΚhΓbG → ΠYKβΝW → ΖjdΗΒg → TPHεΧΤ → Μwovoa → b86ποΛ → κηYΜGE → ΥΟcΘWS → riUΠΓu → lK2τγΑ → ςΗEθe6 → μΣRΤTC → ΩrnwtO → z91υξm → τεCκI4 → πΧΚaP8 → θwYΜoG → Πd7οΘW → θjTΡΒG → ΠnHεxW → Μj9νΒa → δbHεΚK → ΜΘXΝda → fbTΡΚΗ → nYQΥΝy → teAμΗs → βS0φΤM → φΔpuh2 → τM4ςα4 → πξΒi98 → θεIδIG → ΠΛΙbaW → jaWΞΛΓ → haIδΛΕ → ΚaMΩΛc → ΒaWΞΛk → haGζΛΕ → ΞaMΩΛY → ΒfZΛΖk → bQGζΦΛ → ΞuYΜqY → fd3σΘΗ → πUQΥΡ8 → θtlyrG → ΠD1υκW → τΦiΒQ4 → πuIδq8 → θΚ3σbG → πΠXΝV8 → θkeΖΑG → ΠRFηΥW → ΠsiΒsW → jIχχδΓ → εΒOΧjJ → ΚxHεnc → ΜX9νΞa → δgaΚΕK → ΘZNΨΜe → zcSΣΙm → pWCκΟw → Χi6πΓQ → κvJγpE → ΥΘ5ρdS → μrTΡtC → Ωn1υxO → τz9νl4 → πδDιJ8 → θΥΘcRG → ΠsUΠsW → liχχΒΑ → Γz0φlj → φJDιδ2 → τΥΘcR4 → πsUΠs8 → θkχχzG → ηΑVΟkH → ΞjFηΒY → ΠfHεΖW → ΜjPΦΒa → vbHεΚq → ΜY4ςΝa → ξeaΚΗA → δZRΤΜK → ΘrbΙte → XT1υΣΟ → τogΔw4 → πN7οΩ8 → ιηzkGF → ΣΟEθWU → ΣnhΓxU → nL9νβy → δΕAμgK → βΘNΨdM → ΔzTΡli → nLDιβy → ΥΕAμgS → βrNΨtM → Δz1υli → τLDιβ4 → πΥΔgR8 → θsMΩsG → ΠΑχχjW → ΟΒEθjX → ΣhHεΔU → ΜnLαxa → Δb9νΚi → δYKβΝK → ΘΖdΗfe → USPΦΤΣ → vqmxuq