Base 108: 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---
23 cycles1,926×(max) 18 nodes⮎ 0φ → υ1 → σ3 → ο7 → ηF → ΟV → iΒ → Iδ → Ιb → WΞ → gΔ → MΩ → Αj → Gζ → ΝX → eΖ → QΥ → sr ⮌
1,926×(max) 18 nodes⮎ 2τ → ρ5 → λB → ΨN → yl → Cκ → ΦP → up → 4ς → ν9 → γJ → Ηd → SΣ → ov → 6π → ιD → ΤR → qt ⮌
1,926×(max) 18 nodes⮎ 8ξ → εH → ΛZ → aΚ → YΜ → cΘ → UΠ → kz → Eθ → ΡT → mx → Aμ → αL → Γh → Kβ → Εf → OΧ → wn ⮌
31 cycle 215,712×(fixed) (max) 1 node ⮎ rφs ⮌
410 cycles753,954×(max) 9 nodes⮎ KBκγ → ΨΖdO → yRΣm → qBκu → Ψ3ςO → οxl8 → ηBκG → ΨΞVO → yhΒm ⮌
732,139×(max) 9 nodes⮎ C3ςλ → οΧN8 → ηxlG → ΟBκW → ΨhΒO → yJβm → ΗBκe → ΨRΣO → yptm ⮌
728,146×(max) 9 nodes⮎ SBκΤ → ΨptO → y3ςm → οBκ8 → ηΧNG → ΟxlW → iBκΓ → ΨJβO → Ηxle ⮌
727,318×(max) 9 nodes⮎ a3ςΛ → οZΚ8 → ηZΚG → ΟZΚW → iZΚΓ → aJβΛ → ΗZΚe → aRΣΛ → qZΚu ⮌
679,318×(max) 9 nodes⮎ K3ςγ → οΖd8 → ηRΣG → ΟptW → i3ςΓ → οJβ8 → ηΖdG → ΟRΣW → qhΒu ⮌
661,738×(max) 9 nodes⮎ iJβΓ → ΗJβe → ΗRΣe → qRΣu → q3ςu → ο3ς8 → οζF8 → ηΞVG → ΟhΒW ⮌
660,296×(max) 9 nodes⮎ iRΣΓ → qJβu → Η3ςe → οRΣ8 → ηptG → Ο3ςW → οhΒ8 → ηJβG → ΟΖdW ⮌
656,300×(max) 9 nodes⮎ S3ςΤ → οpt8 → η3ςG → οΞV8 → ηhΒG → ΟJβW → ΗhΒe → SJβΤ → Ηpte ⮌
195,684×3 nodes⮎ yBκm → ΨBκO → ΨxlO ⮌
194,004×3 nodes⮎ aBκΛ → ΨZΚO → yZΚm ⮌
52 cycles134,141,834×(fixed) 1 node ⮎ ΛZφΚa ⮌
11,770×(max) 2 nodes⮎ sqφss → sφφφr ⮌
67 cycles1,584,338,572×(max) 176 nodes⮎ CA6ομλ → ιβΧNKE → ΤΖxleS → qRBκΤu → Ψr3ςsO → οy0υl8 → υηCιF2 → σΦΟUP4 → οvjzo8 → ηG6οζG → ιΟΝWVE → ΤjfΔΑS → qOGεΧu → Νx3ςmY → οeAλΖ8 → ηαQΤLG → ΟΔrrgW → iMφφΨΓ → ΩΒJβiN → ΗΑIγje → ΙSGεΣc → ΝpVΞuY → ie4ρΖΓ → νRJβΤA → γΗqsdK → ΗT1τΡe → σnRΣw4 → οq8νt8 → ηε2σHG → ρΟΛYV6 → λjbΘΑC → ΨWGεΞO → ΝygΓlY → eMCιΩΗ → ΦΒRΣiQ → uqIγtq → Ι42σςc → ρξVΞ86 → λζhΒGC → ΨΞJβWO → ΗygΓle → SMCιΩΤ → ΦΒptiQ → uJ3ςγq → οΘ3ςc8 → οηUΟF8 → ηΠjzUG → ΟlFζyW → ΟiCιΒW → ΦiIγΒQ → ΙuIγpc → ΙW4ρΞc → νhVΞΓA → γiKαΒK → ΗΕIγfe → ΙSOΦΣc → wpVΞuo → i84ρξΓ → νζJβGA → γΞΖdWK → ΗhRΣΓe → qSKαΣu → Εp3ςug → οO4ρΧ8 → νηwmFA → γΠ9μUK → γΗkydK → ΗTDθΡe → ΤnRΣwS → rp8νut → ε51τρI → σμΚZA4 → οβZΚK8 → ηΖZΚeG → ΟaQΤΚW → siYΛΒs → cIφφγΙ → δΘHδcJ → ΛΙUΟba → kaWΝΚΑ → gZFζΛΕ → ΟbNΧΙW → yiWΝΒm → gJBκγΕ → ΨΘNΧcO → zxUΟml → kEAλθΑ → αΣFζSM → ΟΓouhW → iL5παΓ → λΔJβgC → ΨΗMΨdO → ΑySΡlk → oGCιζw → ΦΞ7ξWQ → ηugΓpG → ΟM4ρΩW → νΒhΒiA → γKIγβK → ΙΗΕedc → WTPΥΡΟ → unhΒwq → K93ςνγ → οδΖdI8 → ηΚRΣaG → ΟqYΛtW → ic2σΘΓ → ρVJβΟ6 → λΗiΑdC → ΨTHδΡO → Λymwla → aD9μιΛ → γΥZΚQK → ΗtZΚqe → aS2σΣΛ → ρpZΚu6 → λa4ρΚC → νΨYΛNA → γzbΘkK → ΗWEηΞe → ΡhRΣΓU → qmKαxu → ΕB3ςλg → οΩNΧM8 → ηΒxliG → ΟJBκγW → ΨΘhΒcO → yVJβΟm → ΗjBκΑe → ΨSGεΣO → ΝyoulY → eD5πιΗ → λΥRΣQC → ΨtptqO → y42σςm → ρξBκ86 → λζΧNGC → ΨΞxlWO → yhBκΓm → ΨLBκαO → ΨΔxlgO → yNBκΨm → ΨzBκkO → ΨyEηlO → ΡyCιlU → ΦmCιxQ → ΦuAλpQ → αu4ρpM → νΓ4ρhA → νγKαJA → γΘΔfcK → ΗVNΧΟe → yjRΣΑm → qHBκεu → ΨΜ3ςYO → οycΗl8 → ηUCιΠG → ΦΟkyVQ → ujDθΑq → ΤH3ςεS → οΜptY8 → ηd3ςΗG → οΟSΡV8 → ηoiΑvG → ΟI6οδW → ιΚhΒaE → ΤZJβΛS → ΗqaΙte → YS2σΣΝ → ρpdΖu6 → λS4ρΣC → νΨouNA → γz5πkK → λΗEηdC → ΨΡSΡTO → yomwvm ⮌
741,383,102×7 nodes⮎ cJFζγΙ → ΟΘVΞcW → jhUΟΓΒ → kLHδαΑ → ΛΔFζga → ΟaMΨΚW → ΑiYΛΒk ⮌
128,158,058×38 nodes⮎ OJBκγΨ → ΨΘxlcO → yVBκΟm → ΨjBκΑO → ΨyGεlO → ΝyCιlY → ΦeCιΖQ → ΦuQΤpQ → us4ρrq → ν40υςA → υξβJ82 → σζΖdG4 → οΞRΣW8 → ηqgΓtG → ΟM2σΩW → ρΒhΒi6 → λKIγβC → ΨΙΕebO → yXPΥΝm → ufBκΕq → ΨP3ςΦO → οyuol8 → ηD5πιG → λΥΞVQC → ΨthΒqO → yK2σβm → ρΖBκe6 → λΨQΤNC → ΨzrrkO → yEφφηm → θxVΞmF → ΡiAλΒU → αmIγxM → ΙΓAλhc → αWKαΞM → ΕΓgΓhg → OMKαΩΨ → ΕΒxlig ⮌
67,777,718×43 nodes⮎ jh0υΓΒ → υLHδα2 → σΛΓgZ4 → οbLΩΙ8 → ηΓWΝhG → ΟgKαΔW → ΕiMΨΒg → ΑOIγΧk → ΙxFζmc → ΟWAλΞW → αigΓΒM → ΓMIγΩi → ΙΒJβic → ΗWIγΞe → ΙhRΣΓc → qWKαΞu → Εh3ςΓg → οOKαΧ8 → ηΕwmfG → ΟP9μΦW → γvhΒoK → ΗK6οβe → ιΖRΣeE → ΤqQΤtS → sq2σts → ρ2φφσ6 → τπ1τ63 → σριC54 → ομΥPA8 → ηβtpKG → ΟΖ3ςeW → οiQΤΒ8 → ηsIγrG → ΟΙ0υbW → υiWΝΒ2 → σgIγΔ4 → οΙMΨb8 → ηΑWΝjG → ΟgGεΔW → ΝiMΨΒY → ΑeIγΖk → ΙRFζΤc → ΟrVΞsW ⮌
2,627,004×18 nodes⮎ aM6οΩΛ → ιΒZΚiE → ΤaIγΚS → ΙqYΛtc → cW2σΞΙ → ρhVΞΓ6 → λiKαΒC → ΨΕIγfO → ΙyOΦlc → wWCιΞo → Φh7ξΓQ → ηuKαpG → ΟΕ4ρfW → νiOΦΒA → γwIγnK → ΙΗ8νdc → εWSΡΞI → ΛogΓva ⮌
2,274,044×4 nodes⮎ ΟX1τΝW → σieΕΒ4 → οQIγΥ8 → ηΙsqbG ⮌
2,970×(fixed) 1 node ⮎ srφφrs ⮌
7+---Not showing digit sets 7+ due to verbosity.