Base 98: Cycles Sequences: All Cycle Counts

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)		 Frequency Cycle
Length		 Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
27 cycles1,455×(max) 15 nodes⮎ 0μ → λ1 → ι3 → ε7 → ΦF → ΕV → YΒ → SΘ → ev → GΥ → ΓX → UΖ → az → OΜ → mn ⮌
1,455×(max) 15 nodes⮎ 4θ → γ9 → ΡJ → wd → IΣ → yb → MΞ → qj → 6ζ → ΨD → ΙR → gt → CΩ → ΛP → kp ⮌
485×5 nodes⮎ 2κ → η5 → αB → ΝN → ol ⮌
485×5 nodes⮎ 8δ → ΤH → ΑZ → QΚ → ir ⮌
485×5 nodes⮎ EΧ → ΗT → cx → KΠ → uf ⮌
291×3 nodes⮎ Aβ → ΟL → sh ⮌
97×(fixed) 1 node ⮎ WΔ ⮌
31 cycle 161,602×(fixed) (max) 1 node ⮎ mμn ⮌
414 cycles319,432×(max) 21 nodes⮎ YTΖΓ → cTΖy → cLΞy → sLΞi → s9βi → Ρ9βK → ΡvdK → wHΣe → ΑHΣa → ΑPΚa → kPΚq → k5ζq → α5ζC → αΜNC → ΝnlO → o1κm → ι1κ4 → ιδ74 → εΥF8 → ΦΔVG → ΕXΒW ⮌
317,105×(max) 21 nodes⮎ 61κη → ιΩB4 → εΜN8 → ΦnlG → Ε1κW → ιXΒ4 → εTΖ8 → ΦbxG → ΕLΞW → sXΒi → U9βΗ → ΡbxK → wLΞe → sHΣi → Α9βa → ΡPΚK → wjpe → I5ζΤ → αzZC → ΝPΚO → ojpm ⮌
315,636×(max) 21 nodes⮎ A5ζγ → αΠJC → ΝvdO → oHΣm → Α1κa → ιPΚ4 → εjp8 → Φ5ζG → αΔVC → ΝXΒO → oTΖm → c1κy → ιLΞ4 → εrh8 → Φ9βG → ΡΔVK → wXΒe → UHΣΗ → Αbxa → QLΞΛ → sjpi ⮌
312,950×(max) 21 nodes⮎ E5ζΨ → αΘRC → ΝftO → oDΧm → Ι1κS → ιft4 → εDΧ8 → ΦΘRG → ΕftW → YDΧΓ → ΙTΖS → gbxu → MDΧΟ → ΙrhS → g9βu → ΡDΧK → ΙvdS → gHΣu → ΑDΧa → ΙPΚS → kftq ⮌
312,684×(max) 21 nodes⮎ A1κγ → ιΠJ4 → εvd8 → ΦHΣG → ΕzZW → YPΚΓ → kTΖq → c5ζy → αLΞC → ΝrhO → o9βm → Ρ1κK → ιvd4 → εHΣ8 → ΦzZG → ΕPΚW → kXΒq → U5ζΗ → αbxC → ΝLΞO → snli ⮌
312,560×(max) 21 nodes⮎ E1κΨ → ιΘR4 → εft8 → ΦDΧG → ΙΔVS → gXΒu → UDΧΗ → ΙbxS → gLΞu → sDΧi → Ι9βS → ΡftK → wDΧe → ΙHΣS → Αfta → QDΧΛ → ΙjpS → g5ζu → αDΧC → ΝΘRO → oftm ⮌
312,038×(max) 21 nodes⮎ I1κΤ → ιzZ4 → εPΚ8 → ΦjpG → Ε5ζW → αXΒC → ΝTΖO → obxm → M1κΟ → ιrh4 → ε9β8 → ΦΠJG → ΕvdW → YHΣΓ → ΑTΖa → cPΚy → kLΞq → s5ζi → α9βC → ΡΜNK → wnle ⮌
311,286×(max) 21 nodes⮎ E9βΨ → ΡΘRK → wfte → IDΧΤ → ΙzZS → gPΚu → kDΧq → Ι5ζS → αftC → ΝDΧO → ΙnlS → g1κu → ιDΧ4 → εΘR8 → ΦftG → ΕDΧW → ΙXΒS → gTΖu → cDΧy → ΙLΞS → sfti ⮌
310,724×(max) 21 nodes⮎ MHΣΟ → Αrha → Q9βΛ → ΡjpK → w5ζe → αHΣC → ΝzZO → oPΚm → k1κq → ι5ζ4 → εΩB8 → ΦΜNG → ΕnlW → Y1κΓ → ιTΖ4 → εbx8 → ΦLΞG → ΕrhW → Y9βΓ → ΡTΖK → wbxe ⮌
309,206×(max) 21 nodes⮎ M9βΟ → ΡrhK → w9βe → ΡHΣK → Αvda → QHΣΛ → Αjpa → Q5ζΛ → αjpC → Ν5ζO → αnlC → Ν1κO → ιnl4 → ε1κ8 → ιΥF4 → εΔV8 → ΦXΒG → ΕTΖW → cXΒy → ULΞΗ → sbxi ⮌
306,196×(max) 21 nodes⮎ Q1κΛ → ιjp4 → ε5ζ8 → αΥFC → ΝΔVO → oXΒm → U1κΗ → ιbx4 → εLΞ8 → ΦrhG → Ε9βW → ΡXΒK → wTΖe → cHΣy → ΑLΞa → sPΚi → k9βq → Ρ5ζK → αvdC → ΝHΣO → Αnla ⮌
302,815×(max) 21 nodes⮎ I9βΤ → ΡzZK → wPΚe → kHΣq → Α5ζa → αPΚC → ΝjpO → o5ζm → α1κC → ιΜN4 → εnl8 → Φ1κG → ιΔV4 → εXΒ8 → ΦTΖG → ΕbxW → YLΞΓ → sTΖi → c9βy → ΡLΞK → wrhe ⮌
298,825×(max) 21 nodes⮎ M5ζΟ → αrhC → Ν9βO → ΡnlK → w1κe → ιHΣ4 → εzZ8 → ΦPΚG → ΕjpW → Y5ζΓ → αTΖC → ΝbxO → oLΞm → s1κi → ι9β4 → εΠJ8 → ΦvdG → ΕHΣW → ΑXΒa → UPΚΗ → kbxq ⮌
41,370×3 nodes⮎ gDΧu → ΙDΧS → ΙftS ⮌
52 cycles83,281,872×(max) 4 nodes⮎ ΔVμΔX → ΕVμΔW → ΕXμΒW → ΔWμΓX ⮌
9,700×2 nodes⮎ nlμnn → nμμμm ⮌
613 cycles1,409,725,043×(max) 179 nodes⮎ IC0λΩΤ → 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 ⮌
13,620,549×22 nodes⮎ gUAαΖu → ΟbDΧyM → ΙsMΝhS → qgAαtk → ΟD5ζΨM → αΚrhQC → Νj9βqO → Ρo6εlK → Ψw2ιdE → ηΙIΡR6 → αygsbC → ΝNBΩΝO → ΝpnlkO → o51κηm → ιβ1κA4 → ιεΟK74 → εΧtfE8 → ΦΘDΧSG → ΙΕeuVS → gZFΥΑu → ΕRDΧΙW → ΙhXΒsS ⮌
1,414,880×7 nodes⮎ gU0λΖu → λbDΧy2 → ιΙMΝR4 → εqgsj8 → ΦC6εΩG → ΨΜΔVOE → ΙnXΒmS ⮌
1,328,106×6 nodes⮎ iMAαΞs → Οr9βiM → Ρs8γhK → ΤwAαdI → ΟΑIΡZM → ysQΙhc ⮌
1,116,930×6 nodes⮎ c2μμιy → κxXΒc3 → ηUKΟΖ6 → αuayfC → ΝOEΦΜO → ΗommlU ⮌
954,559×5 nodes⮎ ΕΓ0λXW → λYUΕΒ2 → ιaSΗz4 → εeOΛv8 → ΦmGΤnG ⮌
334,004×5 nodes⮎ Ιy4ηbS → γgMΝtA → ΡqCΨjK → Λw6εdQ → ΨkIΡpE ⮌
322,740×5 nodes⮎ ΗΑ2ιZU → ηcQΙx6 → αiKΟrC → Νu8γfO → ΤoEΦlI ⮌
317,736×5 nodes⮎ Νi8γrO → Τo8γlI → ΤΑ2ιZI → ηΑQΙZ6 → αiQΙrC ⮌
317,376×5 nodes⮎ Ηc2ιxU → ηcKΟx6 → αuKΟfC → ΝuEΦfO → ΗoEΦlU ⮌
315,684×5 nodes⮎ Ηo8γlU → Τc2ιxI → ηΑKΟZ6 → αuQΙfC → ΝiEΦrO ⮌
70,180×(fixed) 1 node ⮎ ΟsAαhM ⮌
2,450×(fixed) 1 node ⮎ nmμμmn ⮌
71 cycle 21,243,342,022×(max) 4 nodes⮎ ΜmMμΝnP → ΞnOμΛmN → ΝpNμΜkO → ΝoQμΙlO ⮌
8+---Not showing digit sets 8+ due to verbosity.