Base 126: 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--
29 cycles7 nodesKτ → Ψf → gΧ → eΩ → iΥ → aδ → qΜ
31 cycle (fixed) 1 node ΑОΒ
483 cycles6 nodesUHφλ → εΔxa → s5ИΛ → ГHφC → ρδZO → ΡrΚm
52 cycles2 nodesΒzОΒΒ → ΒОООΑ
654 cycles133 nodesUD9ДБλ → υξΔxQK → αΜ5Иqe → ГkKσΣC → ρΨWηfO → ΡygΦΔm → eU4Йκα → ЕΔjΣyA → υY4ЙζK → ЕαuΗdA → υlBВΡK → ραUιdO → ΡΓkΡzm → WU2Лκι → ЙΔzΒy6 → Г51МЙC → ЛДπNA4 → ЗτΠlK8 → ωΩTκeG → ιΕiΤxW → Αa6ЗδΓ → Бr1МΛE → ЛνIυR4 → ЗγΙsb8 → ωpFψΝG → κθMρWV → ΤΓyΓzk → Y42ЛКη → ЙЖvΖ86 → Гψ9ДGC → υρηWNK → αΣxΔke → kX5ИηΤ → ГxXζΕC → ρw6ЗΖO → БΡ8ЕlE → χνUιRI → εΚΒzsa → sH1МχΛ → ЛζHφY4 → ЗεuΗZ8 → ωtBВΙG → ριEωVO → λΡΑΑlU → ΕUООιy → κΔRμyV → ΙΓ4Йzu → ЕE2ЛАA → ЙυλSJ6 → ГβΖvcC → ρn9ДΟO → υΡQνlK → αΛUιre → ΓkIυΣΑ → γX1Мηc → ЛxnΞΕ4 → ЗQ6Зξ8 → БωΛqFE → νκJτUS → αΙΓyte → kF3КωΤ → ЗκXζU8 → ωΔvΖyG → ιA4ЙДW → ЕτzΒKA → υΩ1МeK → ЛαiΤd4 → ЗlZδΡ8 → ωsUιΚG → ιΓGχzW → ηΑ2ЛΒY → Йw0НΖ6 → НГ8ЕB2 → ЛχρMH4 → ЗζΣjY8 → ωvXζΗG → ιwAГΖW → σΑ8ЕΒM → χΦ0НhI → НεcαZ2 → ЛtlΠΙ4 → ЗUEωκ8 → ωλΓyTG → ιΖ3КwW → ЗΑ8ЕΒ8 → ωχ0НHG → НιεYV2 → ЛΒtΘΑ4 → ЗE0НА8 → НωλSF2 → ЛκΖvU4 → ЗΔ9Дy8 → ωυ4ЙJG → ЕιαcVA → υΒlΠΑK → αU0Нκe → НΔjΣy2 → ЛY4Йζ4 → ЗЕuΗ98 → ωφBВIG → ριγaVO → ΡΒpΜΑm → UM0Нςλ → НΥΔxi2 → Лb5Иγ4 → ЗГoΝB8 → ωςNπMG → ιΥΠliW → ΑbTκγΓ → Εp1МΝy → ЛN5Иρ4 → ЗГΡkB8 → ωςVθMG → ιΥzΒiW → Αb1МγΓ → Лp1МΝ4 → ЛЗMρ74 → ЗАΣjE8 → ωμXζSG → ιΘvΖuW → ΑD9ДБΓ → υξ1МQK → ЛαΛqd4 → ЗlJτΡ8 → ωαUιdG → ιΓkΡzW → ΑW2ЛθΓ → Йz1МΓ6 → ЛГ2ЛB4 → ЙЗρM76 → ГАΣjEC → ρμXζSO → ΡΘvΖum