Base 118: 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--
25 cycles24 nodes2Д → Б5 → υB → ιN → Ιl → Mκ → Λj → Qζ → Γr → Aφ → λL → Νh → Uβ → uz → 4В → χ9 → νJ → Ρd → cΣ → eΠ → aΥ → iΜ → Sδ → yv
31 cycle (fixed) 1 node wЖx
414 cycles29 nodesA5Аχ → υμJC → ιΠdO → ΙbΣm → gLκΟ → ΝXΧi → oTβΗ → wHξy → Φ1Дa → ГjΚ4 → ωPζ8 → ρΔpG → αDςW → εrΒS → Α9φu → ν5АK → υΠdC → ιbΣO → ΙfΞm → YLκΨ → ΝnΖi → UHξγ → Φvxa → k1ДΛ → ГPζ4 → ωΔp8 → ρDςG → εΩVS → ΑrΒu
53 cycles4 nodesΡcЖΡe → ΣbЖΣd → ΤdЖΠc → ΣeЖΟd
66 cycles188 nodesA86ωψχ → σπμJGE → εΩΠdWS → ΑrbΣΓu → gB5АυΟ → υκXΧMC → ιΜnΖiO → ΙTHξγm → ΦxLκwa → Νk0ЕΚi → ЕUOηβ2 → ГΗuyn4 → ωJ3Вν8 → ωρΡcF8 → ρβdΠUG → αvbΣyW → sg2ГΞΓ → БX9φΨ6 → υνoΕJC → ιΣFπcO → αΙeΟlW → saMιΥΓ → Λj9φΛk → νRPζεK → ΡΕΑspe → cF7ψρΤ → ρβfΞUG → αvXΧyW → so2ГΖΓ → БH9φο6 → υνΦYJC → ιΣlΘcO → ΙfLκΟm → ΝZLκΦi → ΝlTβΙi → wUMιβy → Λv1Дyk → ГQ2Гζ4 → БωΓq76 → υςBτEC → κθγSON → ΛΘxvmk → QL1Дλη → ГΞΔpg4 → ωXDςΨ8 → ρεoΕRG → αΒFπsW → αs8χΒW → οs8χΒI → οΦ8χZI → οΦkΙZI → ΦlNθΙa → ΙkMιΚm → ΛPLκηk → ΝΖPζoi → ΕUGοβq → ΨvDςyY → εo2ГΖS → БΑGοt6 → υΨ6ωXC → σιoΕNE → εΚFπkS → αΑOηtW → Ηs6ωΒo → σI8χξE → οεΤaRI → ΦΒhΜsa → kU8χβΛ → οvPζyI → ΦΕ2Гpa → БkEρΚ6 → υγOηTC → ιΗwwnO → ΙIЖЖνm → ξΘRδmJ → ΤΑKλtc → Οg6ωΞg → σYWΨΧE → εqmΗΔS → ΑKCσμu → ηΠ5АeQ → υΕaΤpC → ιiEρΜO → γΙSγlU → ywMιxw → Λ20ЕДk → ЕВPζ42 → ГψΔp84 → ωπDςG8 → ρεΨWRG → αΒpΔsW → sE8χςΓ → οδ9φSI → νΦyuZK → Ρl3ВΙe → ωcMιΣ8 → ρΛeΟjG → αaQεΥW → ΓsiΛΒs → SA8χφε → ομztKI → ΦΠ5Аea → υkaΤΚC → ιiOηΜO → ΙΗSγnm → yMIνκw → ΤΜ1Дic → ГgSγΞ4 → ωyWΨv8 → ρq2ГΔG → БαCσV6 → υηsΑPC → ιΖ7ψoO → ρΙGοlG → αΨMιXW → ΛsoΕΒk → QG8χπη → οΩΔpWI → ΦrDςΓa → εkAυΚS → λΑOηtM → ΝΗ6ωni → σUIνβE → εΤuybS → Αh3ВΝu → ωV5Аα8 → υρsΑFC → ιβ7ψUO → ρΙuylG → αN3ВιW → ωΚrΒk8 → ρP9φηG → ναΕoVK → ΡtFπΑe → αc6ωΣW → σseΟΒE → εa8χΥS → οΑiΛtI → ΦS6ωδa → σzjΚuE → εQ4БζS → χΔztqA → νD5АσK → υζΠdQC → ιΔbΣqO → ΙgCσΞm → ηXLκΨQ → ΝΕoΕpi → UGEρπγ → γΩvxWU → wr1ДΓy → ГB1Дυ4 → ГωιM74 → ωςΚjE8 → ρδPζSG → αΕyupW → sF3ВρΓ → ωβ9φU8 → ρνuyJG → αΣ3ВcW → ωseΟΒ8 → ρa8χΥG → οαiΛVI → ΦtRδΑa → Αk6ωΚu → σP5АηE → υεΕoRC → ιΒFπsO → αΙ8χlW → οsMιΒI → ΦΛ8χja → οkQεΚI → ΦΓOηra → ΗkAυΚo → λPHξηM → ΦΝΕoha → kVFπαΛ → αtPζΑW → Εs6ωΒq → σE8χςE → οεγSRI → ΦΒxvsa → k91ДχΛ → ГξPζI4 → ωΥΔpa8 → ρjDςΛG → εαQεVS → ΓΑsΑts