Base 100: 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---
21 cycle 4,950×(max) 50 nodes0ξ → ν1 → λ3 → η7 → ΨF → ΗV → aΒ → QΜ → kr → 6θ → αD → ΛR → it → Aδ → ΡL → uh → Cβ → ΝP → mp → 2μ → ι5 → γB → ΟN → ql → 4κ → ε9 → ΤJ → yd → KΣ → wf → GΧ → ΕX → WΖ → YΔ → UΘ → cz → MΠ → sj → 8ζ → ΦH → ΓZ → SΚ → gv → EΩ → ΙT → ex → IΥ → Αb → OΞ → on
31 cycle 171,600×(fixed) (max) 1 node nξo
48 cycles695,082×(max) 10 nodesKBβΤ → ΟxdO → qJΣm → y3κe → ηJΣ8 → ΨxdG → ΗJΣW → yZΒe → SJΣΛ → yhte
686,854×(max) 10 nodesaRΚΓ → iRΚu → iBβu → ΟBβO → ΟplO → q3κm → η3κ8 → ηΧF8 → ΨΖVG → ΗZΒW
680,664×(max) 10 nodesK3κΤ → ηxd8 → ΨJΣG → ΗxdW → aJΣΓ → yRΚe → iJΣu → yBβe → ΟJΣO → yple
678,311×(max) 10 nodesC3κγ → ηΞN8 → ΨplG → Η3κW → ηZΒ8 → ΨRΚG → ΗhtW → aBβΓ → ΟRΚO → qhtm
647,216×(max) 10 nodesSBβΛ → ΟhtO → qBβm → Ο3κO → ηpl8 → Ψ3κG → ηΖV8 → ΨZΒG → ΗRΚW → iZΒu
619,908×(max) 10 nodesa3κΓ → ηRΚ8 → ΨhtG → ΗBβW → ΟZΒO → qRΚm → i3κu → ηBβ8 → ΨΞNG → ΗplW
357,000×5 nodesS3κΛ → ηht8 → ΨBβG → ΟΖVO → qZΒm
56,140×(fixed) 1 node yJΣe
53 cycles61,214,090×3 nodesΕVξΖY → ΗWξΕW → ΖZξΒX
30,738,232×(max) 4 nodesΕWξΕY → ΖVξΖX → ΗXξΔW → ΖYξΓX
10,098×2 nodesomξoo → oξξξn
67 cycles735,812,550×(max) 196 nodesKGCαΧΤ → ΝΖxdWQ → mZJΣΓq → yT3κΙe → ηfJΣw8 → ΨyGΦdG → ΗΕKΡXW → waWΕΒg → YRFΧΛΕ → ΗjVΖsW → bZ8εΓΒ → ΦTPΜΙI → Γmewpa → SI2λΥΛ → ιΒhta6 → γRBβΛC → ΠΞisON → sp9δmk → Τ82λζK → ιΧxdG6 → γΖJΣWC → ΟyYΓdO → qUKΡΘm → wd3κyg → ηLFΧΡ8 → ΨΗugVG → ΗbDΩΑW → ΛaOΝΒS → oiQΛto → kAξξγs → δrXΔkB → ΡW6ηΖM → αuYΓhE → ΛUCαΘS → ΝicytQ → mMAγΠq → Ρt3κiM → ηuAγh8 → ΨΡCαLG → ΝΗugVQ → mbDΩΑq → ΛP3κΝS → ηnhto8 → ΨC0νβG → νΞΖVO2 → λpZΒm4 → ηS2λΚ8 → ιΨguF6 → γΘDΩUC → ΟΛcyRO → qjLΠsm → u93κεi → ηΥBβI8 → ΨΟΑaNG → ΗrPΜkW → ma6ηΒq → αR3κΛE → ηΛisR8 → Ψj9δsG → ΤΗ8εVK → ΦyaΑdI → ΓQKΡΜa → wlRΚqg → iG4ιΧu → εΖBβWA → ΤΟYΓNK → yrTΘke → eK6ηΣy → αxJΣeE → ΛyIΤdS → ΑiKΡtc → wOAγΞg → ΡpFΧmM → Ηu2λhW → ιaCαΒ6 → γΝQΛPC → ΟnjroO → q80νζm → νΧ3κG2 → ληΕW74 → ηΩXΔE8 → ΨΚVΖSG → ΗhZΒuW → aSCαΚΓ → ΝhRΚuQ → miCαtq → ΝB3κγQ → ηΠlpM8 → Ψt3κiG → ηΗAγV8 → ΨΡaΑLG → ΗvPΜgW → maEΨΒq → ΙR3κΛU → ηjdxs8 → ΨK8εΣG → ΦΗweVI → ΓbHΥΑa → ΓSOΝΚa → ohRΚuo → iCξξαu → βtTΘiD → ΝeAγxQ → ΡmIΤpM → Αu2λhc → ιOCαΞ6 → γΝomPC → Οn1μoO → λq0νl4 → νη4ι72 → λεΨE94 → ηΥΘTI8 → ΨΒdxaG → ΗRJΣΛW → yjZΒse → SK8εΣΛ → ΦxhteI → ΓJBβΤa → ΟzRΚcO → qiMΟtm → sB3κγk → ηΠ7ζM8 → ΩΧsiGF → ΙΖ9δWU → ΤeYΓxK → yUIΤΘe → ΑdJΣyc → yOKΡΞe → wpJΣmg → yG2λΧe → ιΖJΣW6 → γyYΓdC → ΟUKΡΘO → wqcylg → MG4ιΧΡ → εΖthWA → ΤZBβΓK → ΟySΙdO → qgKΡvm → wF3κΨg → ηΘFΧU8 → ΨΗcyVG → ΗbLΠΑW → uaOΝΒi → oRBβΛo → ΟiξξsO → ΞtLΠiP → uoAγni → ΡC0νβM → νΞthO2 → λpBβm4 → ηΟ2λN8 → ιΨqkF6 → γΘ5θUC → γΟcyNC → ΟrLΠkO → uq6ηli → αC4ιβE → εΞΚROA → ΤphtmK → yC2λβe → ιΞJΣO6 → γyomdC → ΟL1μΡO → λvplg4 → ηF3κΨ8 → ηΨΗUF8 → ΨΘbzUG → ΗdNΞyW → qaKΡΒm → wR3κΛg → ηjFΧs8 → ΨΗ8εVG → ΦΗaΑVI → ΓbPΜΑa → mSOΝΚq → oh3κuo → ηCξξα8 → ζβ5θC9 → γΦΝOHC → ΟΔnnYO → qUξξΗm → ΘpFΧmV → Ηc2λzW → ιaMΟΒ6 → γsQΛjC → Οk8εrO → Φq6ηlI → αΓ4ιZE → εΛSΙRA → ΤjfvsK → yG8εΧe → ΦΖJΣWI → ΓyYΓda → USKΡΚΙ → whdxug
423,765,354×121 nodesQG4ιΧΝ → εΖlpWA → ΤZ3κΓK → ηySΙd8 → ΨgKΡvG → ΗwEΨfW → ΙaGΦΒU → ΕeQΛxY → kWIΤΖs → ΑZ7ζΓc → ΨTNΞΙG → ΗqewlW → aI4ιΥΓ → εΒRΚaA → ΤiQΛtK → ykAγre → ΡK6ηΣM → αxtheE → ΛJBβΤS → ΟzhtcO → qNBβΟm → Οr3κkO → ηq6ηl8 → αΨ4ιFE → εΛΗURA → ΤjbzsK → yO8εΞe → ΦpJΣmI → Γy2λda → ιSKΡΚ6 → γwgufC → ΟHDΩΦO → ΛΔplYS → iV3κΗu → ηbBβΑ8 → ΨΟOΝNG → ΗrnnkW → a6ξξηΓ → θΒRΚa7 → αiQΛtE → ΛkAγrS → Ρi6ηtM → αuAγhE → ΡΛCαRM → ΝuishQ → mD9δαq → ΤΜ3κQK → ηykqd8 → ΨL5θΡG → γΗugVC → ΟbDΩΑO → ΛqOΝlS → oi4ιto → εAξξγA → δδ1μAB → λΣΠLK4 → ηxthe8 → ΨJBβΤG → ΟΗycVO → qbLΠΑm → uP3κΝi → ηnBβo8 → ΨΟ0νNG → νΗqkV2 → λb5θΑ4 → ηγOΝB8 → ΨΠnnMG → ΗsξξiW → ΖtDΩiX → ΛYAγΔS → ΡiUΗtM → ucAγzi → ΡNBβΟM → ΟuqkhO → qD5θαm → γΜ3κQC → ηΟkqN8 → Ψr5θkG → γΗ6ηVC → αΟaΑNE → ΛrPΜkS → mi6ηtq → αB3κγE → ηΠΚRM8 → ΨthtiG → ΗCAγβW → ΡΞZΒOM → upRΚmi → iC2λβu → ιΞBβO6 → γΟomNC → Οr1μkO → λq6ηl4 → ηα4ιD8 → εΨΛQFA → ΤΘjrUK → yd7ζye → ΨLJΣΡG → ΗyugdW → aLDΩΡΓ → ΛvRΚgS → jhEΨut → ΙD9δαU → ΤΜdxQK → ylJΣqe → yK4ιΣe → εxJΣeA → ΤyIΤdK → ΑyKΡdc → wOKΡΞg → wpFΧmg → ΗG2λΧW → ιΖZΒW6 → γZRΚΓC → ΟiSΙtO → qgAγvm → ΡF3κΨM → ηΘthU8 → ΨdBβyG → ΟΗKΡVO → wqaΑlg
236,398,596×23 nodesaLHΥΡΓ → ΓvRΚga → iSEΨΚu → ΙhBβuU → ΟeCαxO → ΝqIΤlQ → Αm4ιpc → εO2λΞA → ιΤomJ6 → γz1μcC → λΟMΟN4 → ηsqkj8 → Ψ95θεG → γΥΖVIC → ΟΒZΒaO → qSQΛΚm → kh3κus → ηD7ζα8 → ΩΧΛQGF → ΙΖjrWU → eZ7ζΓy → ΨTJΣΙG → ΗyewdW
211,723,139×121 nodesOK0νΣΟ → νxple2 → λJ3κΤ4 → θζyc87 → αΧLΠGE → ΛΖthWS → iZBβΓu → ΟTBβΙO → ΟqewlO → qI4ιΥm → εΒ3κaA → ηΤQΛJ8 → ΨzjrcG → ΗN7ζΟW → ΨrZΒkG → ΗS6ηΚW → αhZΒuE → ΛSCαΚS → ΝigutQ → mEAγΩq → ΡΚ3κSM → ηuguh8 → ΨECαΩG → ΝΚΖVSQ → mhZΒuq → SD3καΛ → ηΜhtQ8 → ΨlBβqG → ΟΗ4ιVO → εqaΑlA → ΤQ4ιΜK → εykqdA → ΤL5θΡK → γyugdC → ΟLDΩΡO → ΛvplgS → iF3κΨu → ηΘBβU8 → ΨΟcyNG → ΗrLΠkW → ua6ηΒi → αRBβΛE → ΟΛisRO → qj9δsm → Τ93κεK → ηΥxdI8 → ΨΒJΣaG → ΗyQΛdW → kaKΡΒs → wR7ζΛg → ΨjFΧsG → ΘΖ8εWV → ΦcYΓzI → ΓUMΟΘa → sdRΚyk → iL7ζΡu → ΨvBβgG → ΟΗEΨVO → ΙqaΑlU → eQ4ιΜy → εlJΣqA → Τy4ιdK → εyKΡdA → ΤwKΡfK → ywGΦfe → ΕKGΦΣY → ΕxVΖeY → aWIΤΖΓ → ΑZRΚΓc → iTNΞΙu → qfBβwm → ΟH3κΦO → ηΔplY8 → ΨV3κΗG → ηΗaΑV8 → ΨbPΜΑG → ΗmOΝpW → oa2λΒo → ιQξξΛ6 → θΜLΠQ7 → αukqhE → ΛD5θαS → γΜhtQC → ΟlBβqO → Οq4ιlO → εq4ιlA → εΤ4ιJA → εΤycJA → ΤzLΠcK → yuMΟhe → sKCαΣk → Νx7ζeQ → ΨmIΤpG → ΗΑ2λbW → ιaOΝΒ6 → γoQΛnC → Οk0νrO → νq6ηl2 → λα4ιD4 → ηεΛQ98 → ΨΥjrIG → ΗΒ7ζaW → ΨaQΛΒG → ΗkQΛrW → ka6ηΒs → αR7ζΛE → ΨΛisRG → Ηj9δsW → Τa8εΒK → ΦyQΛdI → ΓkKΡra → wS6ηΚg → αhFΧuE → ΛΗCαVS → ΝiaΑtQ → mQAγΜq → Ρl3κqM → ηu4ιh8 → εΨCαFA → ΤΝΗUPK → ynbzoe
1,223,884×5 nodesSL3κΡΛ → ηvhtg8 → ΨFBβΨG → ΟΘΖVUO → qdZΒym
417,927×(fixed) 1 node yXJΣΕe
2,550×(fixed) 1 node onξξno
72 cycles21,297,386,934×(max) 19 nodesΝmNξΞpQ → ΟnPξΜoO → ΞpNξΞmP → ΟoQξΛnO → ΞoMξΟnP → ΠpPξΜmN → ΟqOξΝlO → ΞqQξΛlP → ΝnOξΝoQ → ΞmOξΝpP → ΞoPξΜnP → ΝoNξΞnQ → ΟnOξΝoO → ΞqOξΝlP → ΞoQξΛnP → ΝnMξΟoQ → ΠoOξΝnN → ΟrOξΝkO → ΞqRξΚlP
3,072,680,766×(fixed) 1 node ΞoOξΝnP
8+---Not showing digit sets 8+ due to verbosity.