Base 168: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР
СТУФХЦЧШЩЪЫЬЭЮЯа
бвгдежзийклмнопр
стуфхцчшщъыьэюяァ

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 cycles13,026×(max) 78 nodes⮎ 0ш → ч1 → х3 → с7 → йF → ЩV → σΒ → eР → αΥ → 4ф → п9 → еJ → Сd → γΣ → 8р → зH → ХZ → λΚ → Oа → Зn → Ηξ → UЪ → υz → iМ → Ρδ → Aо → гL → Нh → Τβ → 6т → лD → ЭR → Бt → uА → sВ → wψ → oЖ → Επ → YЦ → νΘ → SЬ → ωv → qД → Ατ → gО → ΦΩ → 2ц → у5 → нB → бN → Йl → Λκ → Mв → Лj → Οζ → Eк → ЫT → χx → mИ → Ιμ → QЮ → Гr → yφ → kК → Νθ → Iж → Уb → ηΞ → Gи → ЧX → οΖ → WШ → ρΔ → aФ → ιΜ → Kд → Пf → ΨΧ ⮌
1,002×6 nodes⮎ Cм → ЯP → Еp → Γς → cТ → εΠ ⮌
31 cycle 804,272×(fixed) (max) 1 node ⮎ ΧшΨ ⮌
49 cycles5,318,516×(max) 6 nodes⮎ O7рб → йИlG → ЩΚκW → σNаΓ → ЙdРm → γΚκΤ ⮌
5,018,688×(max) 6 nodes⮎ eNаС → ЙβΣm → Λ7рλ → йNаG → ЩИlW → σΚκΓ ⮌
4,523,966×(max) 6 nodes⮎ u7рБ → йtАG → ЩtАW → σtАΓ → udРБ → γtАΤ ⮌
4,389,496×(max) 6 nodes⮎ γ7рΤ → й7рG → йШVG → ЩςΒW → σdРΓ → γdРΤ ⮌
4,389,486×(max) 6 nodes⮎ ΛdРλ → γNаΤ → Й7рm → йΚκG → ЩNаW → ЙςΒm ⮌
4,366,640×(max) 6 nodes⮎ e7рС → йβΣG → Щ7рW → йςΒG → ЩdРW → σβΣΓ ⮌
2,673,442×3 nodes⮎ uNаБ → ЙtАm → ΛtАλ ⮌
1,856,008×3 nodes⮎ σ7рΓ → йdРG → ЩβΣW ⮌
1,853,400×3 nodes⮎ ΛNаλ → ЙNаm → ЙΚκm ⮌
52 cycles1,182,980,906×(fixed) 1 node ⮎ БtшАu ⮌
28,390×(max) 2 nodes⮎ ΨΦшΨΨ → ΨшшшΧ ⮌
6+---Not showing digit sets 6+ due to verbosity.