Base 98: 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--
27 cycles15 nodes4θ → γ9 → ΡJ → wd → IΣ → yb → MΞ → qj → 6ζ → ΨD → ΙR → gt → CΩ → ΛP → kp
31 cycle (fixed) 1 node mμn
414 cycles21 nodesM5ζΟ → αrhC → Ν9βO → ΡnlK → w1κe → ιHΣ4 → εzZ8 → ΦPΚG → ΕjpW → Y5ζΓ → αTΖC → ΝbxO → oLΞm → s1κi → ι9β4 → εΠJ8 → ΦvdG → ΕHΣW → ΑXΒa → UPΚΗ → kbxq
52 cycles4 nodesΔVμΔX → ΕVμΔW → ΕXμΒW → ΔWμΓX
613 cycles179 nodesIC0λΩΤ → λΜzZO2 → ιnPΚm4 → εk0λp8 → λΦ4ηF2 → ιγΕU94 → εΣZzI8 → ΦzPΚaG → ΕkOΛpW → mY4ηΒo → γT1κΗA → ιΡcwJ4 → εxJΠc8 → ΦwKΟdG → ΕuIΡfW → yYEΦΒc → ΗTLΞΗU → sdbxwi → MJ9βΡΟ → ΡxrhcK → wL9βΟe → ΡtHΣgK → ΑwCΨda → ΛQIΡΚQ → ykiqpc → M84ηδΟ → γΥrhGA → ΡΔ9βWK → ΡwWΓdK → wWIΡΔe → yXHΣΓc → ΑVLΞΕa → sZPΚΑi → kR9βΙq → Ρh5ζsK → αwAαdC → ΟΝIΡNM → ysokhc → MB3θαΟ → εΞrhM8 → Φr9βiG → ΡΕ8γVK → ΤwYΑdI → ΑSIΡΘa → yfPΚuc → kMEΦΞq → Ηr5ζiU → αc8γxC → ΤΝKΟNI → Αuokfa → QF3θΦΛ → εΖjpU8 → Φb5ζyG → αΕMΝVC → ΝqYΑjO → oS6εΘm → Ψf1κuE → ιΙEΦR4 → εΗgsT8 → ΦdBΩwG → ΝΕIΡVO → yoYΑlc → SM2ιΞΙ → ηrfti6 → αE8γΧC → ΤΝΗSNI → Αpdvka → QI4ηΣΛ → γzjpaA → ΡP5ζΛK → αwkodC → ΝJ3θΡO → εxnlc8 → ΦL1κΟG → ιΕsgV4 → εZBΩΑ8 → ΦΝQΙNG → ΕphrkW → YA4ηβΓ → γΠTΖKA → ΡvbxeK → wMGΤΞe → ΓrHΣiY → ΑU8γΖa → ΤbPΚyI → ΑkMΝpa → qQ4ηΚk → γj5ζqA → αΡ6εJC → ΨΝwcNE → ΙpJΠkS → wg4ηte → γICΨΣA → ΡΛyaPK → wlNΜoe → oI2ιΣm → ηz1κa6 → ιαOΛB4 → εΞlnM8 → Φr1κiG → ιΕ8γV4 → εΤYΑH8 → ΦΒRΘYG → ΕgSΗtW → eYCΨΒw → ΛTHΣΗQ → Αkcwpa → QK4ηΠΛ → γvjpeA → ΡH5ζΤK → αΒvdYC → ΝTHΣΗO → Αocwla → QK2ιΠΛ → ηvjpe6 → αH5ζΤC → αΝΑYNC → ΝpRΘkO → og4ηtm → γD1κΨA → ιΡΙQJ4 → εxhrc8 → ΦL9βΟG → ΡΕsgVK → wZBΩΑe → ΝRHΣΙO → Αogsla → QC2ιΩΛ → ηΜjpO6 → αn5ζmC → αΝ0λNC → λΝokN2 → ιp3θk4 → ζδ4η87 → γΨΤGDA → ΡΚΒXQK → wjTΖqe → cI6εΣy → ΨzLΞaE → ΙsOΛhS → mgAαto → ΟD1κΨM → ιΚrhQ4 → εj9βq8 → ΦΡ6εJG → ΨΕwcVE → ΙZJΠΑS → wgQΙte → iICΨΣs → Λz9βaQ → ΡkOΛpK → wm4ηne → γI0λΣA → λΡyaJ2 → ιxNΜc4 → εoKΟl8 → Φu2ιfG → ηΕEΦV6 → αΗYΑTC → ΝdRΘwO → ogIΡtm → yD1κΨc → ιΚLΞQ4 → εsiqh8 → ΦB7δαG → ΦΞΔVMG → ΕrXΒiW → YU8γΖΓ → ΤbTΖyI → ΑcMΝxa → qQKΟΚk → uj5ζqg → αE6εΧC → ΨΝΗSNE → ΙpdvkS → gI4ηΣu → γzDΧaA → ΡΙOΛRK → wmgsne
71 cycle 4 nodesΜmMμΝnP → ΞnOμΛmN → ΝpNμΜkO → ΝoQμΙlO