Base 120: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР

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---
22 cycles6,545×(max) 55 nodes⮎ 0И → З1 → Е3 → Б7 → σF → γV → uΒ → 6В → υD → ηR → Γt → 8А → ρH → ΨZ → mΚ → Mμ → Νj → Sζ → Αv → 4Д → ω9 → οJ → Τd → eΣ → cΥ → gΠ → YΩ → oΘ → Iπ → Φb → iΞ → Uδ → wz → 2Ж → Г5 → χB → λN → Λl → Oκ → Ιn → Kξ → Ρf → aΧ → kΜ → Qθ → Εr → Cφ → ιP → Ηp → Gς → αX → qΖ → Eτ → εT → yx ⮌
595×5 nodes⮎ Aψ → νL → Οh → Wβ → sΔ ⮌
31 cycle 295,120×(fixed) (max) 1 node ⮎ xИy ⮌
47 cycles2,296,214×(max) 4 nodes⮎ O7Аλ → σΚlG → γNκW → ΛtΒm ⮌
1,628,936×(max) 4 nodes⮎ u7АΓ → σ7АG → σβVG → γtΒW ⮌
1,612,788×(max) 4 nodes⮎ uNκΓ → Λ7Аm → σNκG → γΚlW ⮌
1,610,428×(max) 4 nodes⮎ e7АΤ → σdΣG → γdΣW → udΣΓ ⮌
974,328×2 nodes⮎ eNκΤ → ΛdΣm ⮌
637,408×2 nodes⮎ γ7АW → σtΒG ⮌
318,408×(fixed) 1 node ⮎ ΛNκm ⮌
52 cycles225,135,386×(fixed) 1 node ⮎ ΤdИΣe ⮌
14,518×(max) 2 nodes⮎ ywИyy → yИИИx ⮌
66 cycles4,508,889,946×23 nodes⮎ eF7АσΤ → σδdΣUG → γxdΣyW → ue0ЗΣΓ → Зd7АΤ2 → ЕσeΡF4 → БδbΥU8 → σxhΞyG → γW0ЗβW → ЗusΓΒ2 → ЕA6Бψ4 → БυνKD8 → σθΠfQG → γΖZΧqW → umEσΚΓ → εN7АλU → σΜxxkG → γQИИηW → θβ3ДWR → БΕsΓr8 → σD9ψυG → οθβVQK → ΤΖtΒqe ⮌
108,719,200×(max) 61 nodes⮎ cV7АγΦ → σvhΞΑG → γW4ГβW → ωusΓΒA → οA6БψK → υξΣdKE → ηΣdΣeS → ΓecΤΣu → gd7АΤΡ → σfZΧΡG → γmaΦΚW → ukMλΜΓ → ΝR7Аηk → σΔRζsG → γΓAχtW → νu8ωΒM → ρΟ6БhI → υΨWαZE → ηsmΙΔS → ΓMAχμu → νΞ7АiM → σΟUγhG → γwWαzW → us2ЕΔΓ → ГB7Аχ6 → χσλMFC → λδΜjUO → ΛxRζym → ΓO0Зκu → ЗΚ7Аm2 → ЕσMλF4 → БδΜjU8 → σxRζyG → γΓ0ЗtW → Зu8ωΒ2 → Еρ6БH4 → БυΨYD8 → σθnΘQG → γΖJξqW → ΤuEσΒe → εe6БΣU → υycΤxE → ηg0ЗΠS → ЗΓYΨt2 → Еo8ωΘ4 → БρIοH8 → σΩΥbYG → γphΞΗW → uWGρβΓ → αt7АΓY → σq8ωΖG → ργEσVI → εΨuΑZU → yn5ВΙy → χKИИνC → φξ9ψKD → οιΡePK → ΤΘbΥoe → ieIοΣΟ → ΦdVβΤc → uieΡΞΓ ⮌
70,415,762×24 nodes⮎ S86БАη → υςΒtGE → ηβ7АWS → σΓsΓtG → γA8ωψW → ρξtΒKI → ΨΣ7Аea → σmcΤΚG → γgMλΠW → ΝuYΨΒk → oS6БζΙ → υΒJξuE → ηΤ6БdS → υΓeΡtE → ηc8ωΥS → ρΓgΟtI → ΨY8ωΩa → ρplΚΗI → ΨOGρκa → αΚlΚmY → qOMλκΗ → ΝΚFςmk → γSMλζW → ΝΒtΒuk ⮌
1,883,594×4 nodes⮎ Бx3Дy8 → Бσ0ЗF8 → ЗσγUF2 → ЕδvzU4 ⮌
713,218×2 nodes⮎ Бδ1ЖU8 → ЕσwyF4 ⮌
3,660×(fixed) 1 node ⮎ yxИИxy ⮌
7+---Not showing digit sets 7+ due to verbosity.