Base 104: 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---
28 cycles1,236×(max) 12 nodes⮎ 0ς → ρ1 → ο3 → λ7 → γF → ΛV → eΒ → MΥ → wj → Cζ → ΡP → qp ⮌
1,236×(max) 12 nodes⮎ 2π → ν5 → ηB → ΤN → ul → 8κ → αH → ΗZ → WΚ → cΔ → QΠ → or ⮌
1,236×(max) 12 nodes⮎ Aθ → ΦL → yh → Gβ → ΙX → aΖ → UΜ → gz → IΩ → Εb → SΞ → kv ⮌
618×6 nodes⮎ 4ξ → ι9 → ΨJ → Γd → OΣ → sn ⮌
412×4 nodes⮎ 6μ → εD → ΟR → mt ⮌
309×3 nodes⮎ Eδ → ΝT → ix ⮌
206×2 nodes⮎ KΧ → Αf ⮌
103×(fixed) 1 node ⮎ YΘ ⮌
31 cycle 192,816×(fixed) (max) 1 node ⮎ pςq ⮌
43 cycles2,030,860×(max) 6 nodes⮎ O7κΤ → γtlG → Λ7κW → γdΒG → ΛNΣW → udΒm ⮌
1,970,232×(max) 6 nodes⮎ eNΣΓ → uNΣm → u7κm → γ7κG → γΚVG → ΛdΒW ⮌
1,159,414×3 nodes⮎ e7κΓ → γNΣG → ΛtlW ⮌
52 cycles111,458,154×(max) 4 nodes⮎ ΘXςΘZ → ΙXςΘY → ΙZςΖY → ΘYςΗZ ⮌
10,918×2 nodes⮎ qoςqq → qςςςp ⮌
613 cycles1,497,617,828×(max) 227 nodes⮎ GC6λζγ → εΣΚVOE → ΟtdΒmS → mO6λΣu → εt7κmE → γΟ6λRG → εΛmsVE → Οf5μΑS → ηmKΦtC → ΤΑ6λfO → εuKΦlE → ΟΑ8ιfS → αmKΦtI → ΗΑ6λfa → εWKΦΚE → ΟΑcΓfS → mQKΦΠu → Αp7κqg → γK0ρΧG → ρΛΑeV2 → οfLΥΑ4 → λyKΦh8 → γΑGαfG → ΛΙKΦXW → ΑeaΕΒg → UNJΧΤΝ → Γvhxke → OGAηβΤ → ΦΚtlWM → yd7κΓi → γPFβΡG → ΜΚqoWV → gd1πΓΑ → οPJΧΡ4 → λΓqod8 → γP1πΡG → οΛqoV4 → λf1πΑ8 → ογKΦF4 → λΜzfU8 → γhJΧyG → ΛΓGαdW → ΙeOΡΒY → saMΤΖo → wV3ξΛk → λfBζΑ8 → γΤKΦNG → ΛΑukfW → eL9θΦΓ → ΨzNΣgK → ΓuIΨle → ΕO8ιΣc → αtRΞmI → Ηm6λta → εW6λΚE → εΟcΓRE → ΟnPΠsS → qm4νtq → ι6ςςλA → μθ1πA7 → οεΦKD4 → λΠzfQ8 → γpJΧqG → ΛΓ0ρdW → ρeOΡΒ2 → οsMΤn4 → λw4νj8 → ιγCεFA → ΨΡΛUPK → Γrfzoe → OK2οΧΤ → νΒtle6 → ηN7κΤC → γΤukNG → Λv9θkW → ΨeAηΒK → ΦΓMΤdM → ywOΡji → sGCεβo → ΡΚ3ξWQ → λqcΓp8 → γQ0ρΠG → ρΛoqV2 → οf1πΑ4 → ολKΦ74 → λδzfE8 → γΞJΧSG → ΛΓkudW → eP9θΡΓ → ΨrNΣoK → Γu2οle → νO8ιΣ6 → ηαsmHC → ΤΘ5μYO → ηuYΗlC → ΤY8ιΘO → αuYΗlI → ΗY8ιΘa → αZVΚΗI → ΗeWΙΒa → cWMΤΚΕ → wdRΞΓk → mPBζΡu → Τr7κoO → γu2οlG → νΛ8ιV6 → ηαeΑHC → ΤΘLΥYO → yuYΗli → YG8ιβΙ → αΚZΖWI → ΗdVΚΓa → eWOΡΚΓ → sdNΣΓo → uP3ξΡm → λr7κo8 → δβ2οGF → νΝΙWT6 → ηjbΔwC → ΤSCεΞO → ΡukulQ → qA8ιθq → αΦςςKI → ΩΧ3ξKJ → λΕΑeb8 → γTLΥΝG → ΛyiwhW → eHDδαΓ → ΟΘNΣYS → umYΗtm → Y86λκΙ → εβZΖGE → ΟΚVΚWS → mecΓΒu → QN7κΤΡ → γvppkG → ΛAςςηW → θΚJΧWB → ΦΓcΓdM → yQOΡΠi → spFβqo → Λ40ρξW → ρκdΒ82 → οβNΣG4 → λΚtlW8 → γd7κΓG → γΛOΡVG → ΛseΑnW → eM4νΥΓ → ιxNΣiA → ΨuEγlK → ΝΓ8ιdU → αiOΡxI → ΗsEγna → ΝW4νΚU → ιicΓxA → ΨQEγΠK → ΝΓoqdU → iP1πΡy → οrFβo4 → λΛ2οV8 → νγeΑF6 → ηΜLΥUC → ΤygyhO → uIGαΩm → ΙΖ7κaY → γaUΛΖG → ΛgUΛzW → geIΨΒΑ → ΕNJΧΤc → ΓvRΞke → mOAηΣu → Φt7κmM → γy6λhG → εΛGαVE → ΟΙeΑXS → mbLΥΕu → yT7κΝi → γjFβwG → ΜΚCεWV → ΡgcΓzQ → qQIΨΠq → Εoςςqc → ΔrDδod → ΟQ2οΠS → νpltq6 → η80ρκC → ρβΣNG2 → οΚtlW4 → λd7κΓ8 → δβOΡGF → ΝΚrnWU → id3ξΓy → λPFβΡ8 → γΛqoVG → Λf1πΑW → οeKΦΒ4 → λΑMΤf8 → γwKΦjG → ΛΑCεfW → ΡeKΦΒQ → ΑqMΤpg → wK0ρΧk → ρΒBζe2 → οΤMΤN4 → λwukj8 → γD9θεG → ΨΠΚVQK → ΓpdΒqe → PN0ρΤΣ → ρvrnk2 → οB3ξη4 → μκΤM87 → εβvjGE → ΟΚBζWS → ΤmcΓtO → uQ6λΠm → εp7κqE → γΟ0ρRG → ρΛmsV2 → οf5μΑ4 → ληKΦB8 → γΥzfMG → ΛxJΧiW → ΓeEγΒe → ΝOMΤΣU → wthxmk ⮌
217,297,301×17 nodes⮎ YNFβΤΙ → ΛvZΖkW → eWAηΚΓ → ΦdNΣΓM → yuOΡli → sG8ιβo → αΚ3ξWI → λΗcΓZ8 → γXPΠΙG → ΛqaΕpW → eU0ρΜΓ → ρhNΣy2 → οuGαl4 → λΙ8ιX8 → γαaΕHG → ΛΘTΜYW → ieYΗΒy ⮌
145,829,543×52 nodes⮎ C95μιη → ηΩΣNIC → ΤΖtlaO → uV7κΛm → γf7κΑG → γΛKΦVG → ΛΑeΑfW → eMKΦΥΓ → ΑxNΣig → uKEγΧm → ΝΒ7κeU → γiMΤxG → ΛwEγjW → ΝeCεΒU → ΡiMΤxQ → wqEγpk → ΝC0ρζU → ρΣhxO2 → οtFβm4 → λΛ6λV8 → εγeΑFE → ΟΜLΥUS → ymgyti → IG6λβα → εΚΖZWE → ΟdVΚΓS → meOΡΒu → sN7κΤo → γv3ξkG → λΛAηV8 → γΦeΑLG → ΛzLΥgW → yeIΨΒi → ΕNFβΤc → ΛvRΞkW → meAηΒu → ΦN7κΤM → γyukhG → ΛH9θαW → ΨΘdΒYK → ΓZNΣΗe → uXNΣΙm → ub7κΕm → γT7κΝG → γΛiwVG → ΛfDδΑW → ΟeKΦΒS → ΑmMΤtg → wK6λΧk → εΒBζeE → ΤΟMΤRO → wumslk ⮌
127,624,552×42 nodes⮎ M82οκΦ → νβxhG6 → ηΚFβWC → ΤΛcΓVO → ufPΠΑm → qL7κΦq → γyςςgG → βzRΞgH → ΙmIΨtY → Εa6λΖc → εVRΞΛE → ΟmeΑtS → mM6λΥu → εx7κiE → γΟEγRG → ΝΛmsVU → if5μΑy → ηLFβΦC → ΤΛygVO → ufHΩΑm → ΗL7κΦa → γzVΚgG → ΛeIΨΒW → ΕeMΤΒc → wSMΤΞk → wlBζuk → ΤC8ιζO → αΣtlOI → Ηt7κma → γW6λΚG → εΛcΓVE → ΟfPΠΑS → qmKΦtq → Α6ςςλg → μzXΘg7 → εaIΨΖE → ΟΕUΛbS → mgSΝzu → kJ7κΨw → γΔBζcG → ΤΛQΟVO → uoeΑrm ⮌
33,548,708×11 nodes⮎ eXHΩΙΓ → ΗbNΣΕa → uWSΝΚm → kd7κΓw → γPBζΡG → ΤΛqoVO → uf1πΑm → οL7κΦ4 → λγygF8 → γΜHΩUG → ΛΗgyZW ⮌
1,037,946×4 nodes⮎ iM6λΥy → εxFβiE → ΟΛEγVS → ΝmeΑtU ⮌
1,026,664×12 nodes⮎ ΙΗ0ρZY → ρaWΙΖ2 → οcUΛΔ4 → λgQΟz8 → γoIΨrG → ΛΕ2οbW → νeSΝΒ6 → ηkMΤvC → ΤwAηjO → ΦuCεlM → Ρy8ιhQ → αqGαpI ⮌
442,074×6 nodes⮎ Τc4νΔO → ιuQΟlA → Ψo8ιrK → αΓ2οdI → νΗOΡZ6 → ηsWΙnC ⮌
234,850×3 nodes⮎ ΝΓ4νdU → ιiOΡxA → ΨsEγnK ⮌
159,740×2 nodes⮎ ΟΑ6λfS → εmKΦtE ⮌
127,498×2 nodes⮎ ΟY6λΘS → εmYΗtE ⮌
73,800×(fixed) 1 node ⮎ ΝiEγxU ⮌
2,756×(fixed) 1 node ⮎ qpςςpq ⮌
7+---Not showing digit sets 7+ due to verbosity.