Base 92: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

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---
27 cycles910×(max) 10 nodes⮎ 0ζ → ε1 → γ3 → Ψ7 → ΟF → yV → SΒ → Yv → MΘ → kj ⮌
910×(max) 10 nodes⮎ 4β → Φ9 → ΛJ → qd → CΣ → ΕP → ep → AΥ → ΙL → mh ⮌
910×(max) 10 nodes⮎ 6Ω → ΡD → ΓR → at → IΜ → sb → GΞ → wX → OΖ → gn ⮌
455×5 nodes⮎ 2δ → α5 → ΤB → ΗN → il ⮌
455×5 nodes⮎ 8Χ → ΝH → uZ → KΚ → of ⮌
455×5 nodes⮎ EΠ → ΑT → Wx → QΔ → cr ⮌
91×(fixed) 1 node ⮎ Uz ⮌
31 cycle 133,952×(fixed) (max) 1 node ⮎ jζk ⮌
45 cycles651,284×(max) 11 nodes⮎ aJΚu → qJΚe → qBΣe → ΗBΣO → ΗhlO → i3βm → Ψ3β8 → ΨΞF8 → ΟxVG → yRΒW → aRΒu ⮌
639,356×(max) 11 nodes⮎ K3βΛ → Ψpd8 → ΟBΣG → ΗxVO → iRΒm → a3βu → ΨJΚ8 → ΟpdG → yBΣW → ΗRΒO → iZtm ⮌
638,180×(max) 11 nodes⮎ KBΣΛ → ΗpdO → iBΣm → Η3βO → Ψhl8 → Ο3βG → ΨxV8 → ΟRΒG → yZtW → SJΚΓ → qZte ⮌
628,224×(max) 11 nodes⮎ S3βΓ → ΨZt8 → ΟJΚG → ypdW → SBΣΓ → ΗZtO → iJΚm → q3βe → ΨBΣ8 → ΟΖNG → yhlW ⮌
626,409×(max) 11 nodes⮎ C3βΤ → ΨΖN8 → ΟhlG → y3βW → ΨRΒ8 → ΟZtG → yJΚW → qRΒe → aBΣu → ΗJΚO → qhle ⮌
52 cycles61,115,418×(max) 4 nodes⮎ zTζzV → ΑTζzU → ΑVζxU → zUζyV ⮌
8,554×2 nodes⮎ kiζkk → kζζζj ⮌
618 cycles838,588,583×(max) 95 nodes⮎ G51δαΟ → γΥxVA4 → ΨΚRΒK8 → ΟpZteG → yKAΤΚW → ΙpRΒeM → maAΤti → ΙJ3βΛM → Ψrlhc8 → ΟF3βΟG → ΨzxVU8 → ΟVRΒyG → yaSΑtW → YSIΛΒw → sZNΖuc → iLFΞΙm → yn3βgW → ΨS6ΨΒ8 → ΡΟYuFE → ΓzLΘUS → maUyti → UJ3βΛΑ → ΨrVxc8 → ΟSEΟΒG → ΑyYuVU → WTLΘΑy → mXRΒwi → aP3βΕu → ΨfJΚo8 → Οq8ΦdG → ΝyCΡVI → ΕuSΑZQ → eYKΙvq → oNBΣΗg → Ηj7ΧkO → Οi0εlG → εy2γV2 → γαSΑ54 → ΨΥXvA8 → ΟΚNΖKG → yphleW → SB3βΤΓ → ΨΘZtM8 → ΟlJΚiG → yq2γdW → αSCΡΒ6 → ΤΕYuPC → ΗfLΘoO → mi8Φli → Ν42γβI → αΧtZ86 → ΤΞJΚGC → ΗxpdWO → iRBΣΓm → Ηb3βsO → ΨiGΝl8 → Οw2γXG → αyOΕV6 → ΤgSΑnC → ΗY6ΨvO → ΡiMΗlE → Γk2γjS → αa0εt6 → εΤIΛB2 → γΘrbM4 → ΨlFΞi8 → Οy2γVG → αySΑV6 → ΤYSΑvC → ΗYMΗvO → kiMΗlk → k2ζζγk → δjfnk3 → α80εΧ6 → εΤΝGB2 → γΘvXM4 → ΨlNΖi8 → Οi2γlG → αy2γV6 → αΤSΑB6 → ΤΘXvMC → ΗlNΖiO → jh2γml → α51δα6 → γΥΣBA4 → ΨΚΖNK8 → ΟphleG → yB3βΤW → ΨΘRΒM8 → ΟlZtiG → yK2γΚW → αpRΒe6 → ΤaAΤtC → ΙΗIΛNM → smikhc ⮌
89,549,327×8 nodes⮎ oZBΣug → ΗL7ΧΙO → ΟnhlgG → y73βΨW → ΨΠRΒE8 → ΟΒZtSG → yZJΚuW → qSKΙΒe ⮌
27,422,450×24 nodes⮎ OA2γΥΗ → αΚhlK6 → Τp3βeC → ΨΗAΤN8 → ΟΙikLG → yn1δgW → γS6ΨΒ4 → ΨΡYuD8 → ΟΔLΘQG → ymcqhW → SE4αΠΓ → ΦΒZtSA → ΛZJΚuK → rpKΙed → oEAΤΠg → ΙΒ7ΧSM → ΟmYuhG → yM4αΘW → ΦlRΒiA → Λa2γtK → αqIΛd6 → ΤsCΡbC → ΗΕGΝPO → wieolY ⮌
16,451,152×35 nodes⮎ YUQΓzw → cVNΖys → iTFΞΑm → yX3βwW → ΨSOΕΒ8 → ΟgYunG → yM6ΨΘW → ΡlRΒiE → Γa2γtS → αaIΛt6 → ΤsIΛbC → ΗsGΝbO → wiGΝlY → wO2γΖY → αhNΖm6 → Τi4αlC → ΦΗ2γNA → αΛikJ6 → Τr1δcC → γΗEΟN4 → ΨΑikT8 → ΟX1δwG → γyOΕV4 → ΨgSΑn8 → ΟY6ΨvG → ΡyMΗVE → ΓkSΑjS → aY0εvu → εNJΚΗ2 → γqikd4 → ΨD1δΡ8 → γΟΓQF4 → ΨzbrU8 → ΟVFΞyG → zxSΑWV ⮌
8,070,362×43 nodes⮎ SECΡΠΓ → ΕΒZtSQ → eZJΚuq → qLBΣΙe → ΗnBΣgO → Ηi6ΨlO → Ρi2γlE → αΓ2γR6 → αΤasB6 → ΤΘHΜMC → ΗukiZO → iL1δΙm → γn3βg4 → ΩΧ6Ψ87 → ΣΠΝGED → ΕΒvXSQ → eZNΖuq → iLBΣΙm → Ηn3βgO → Ψi6Ψl8 → ΡΟ2γFE → αΓyUR6 → ΤbTzsC → ΗWGΝxO → wiQΓlY → cO2γΖs → αhFΞm6 → Τy4αVC → ΦΗSΑNA → ΛjXvkK → qO0εΖe → εhBΣm2 → γΗ4αN4 → ΨΦik98 → ΟΜ1δIG → γysaV4 → ΨTHΜΑ8 → ΟuWwZG → yQKΙΔW → odRΒqg → aD7ΧΡu → ΟΔJΚQG → yqcqdW ⮌
3,775,071×20 nodes⮎ mYKΙvi → oN3βΗg → Ψj7Χk8 → ΠΞ0εGF → εΑwWT2 → γXPΔw4 → ΨeOΕp8 → ΟgAΤnG → Ιy6ΨVM → ΡmSΑhE → ΓY4αvS → ΦaMΗtA → ΛkIΛjK → sq0εdc → εGCΡΞ2 → γΕwWP4 → ΨfPΔo8 → Οe8ΦpG → ΝyAΤVI → ΙuSΑZM ⮌
775,528×4 nodes⮎ oS8ΦΒg → ΝZ7ΧuI → ΟuKΙZG → yoKΙfW ⮌
667,166×4 nodes⮎ kaGΝtk → wIζζΛY → ΜvDΠYJ → ΓsMΗbS ⮌
649,636×5 nodes⮎ ΑmCΡhU → ΕW4αxQ → ΦeQΓpA → ΛcAΤrK → ΙqEΟdM ⮌
393,929×5 nodes⮎ Αy0εVU → εWSΑx2 → γYQΓv4 → ΨcMΗr8 → ΟkEΟjG ⮌
282,410×5 nodes⮎ Εu4αZQ → ΦeKΙpA → ΛoAΤfK → Ιq8ΦdM → ΝmCΡhI ⮌
275,796×5 nodes⮎ Ηo8ΦfO → Νi8ΦlI → Νu2γZI → αuKΙZ6 → ΤoKΙfC ⮌
267,530×5 nodes⮎ Γw2γXS → αaOΕt6 → ΤgIΛnC → Ηs6ΨbO → ΡiGΝlE ⮌
259,236×5 nodes⮎ Αu2γZU → αWKΙx6 → ΤoQΓfC → Ηc8ΦrO → ΝiEΟlI ⮌
256,356×5 nodes⮎ Αi8ΦlU → ΝW2γxI → αuQΓZ6 → ΤcKΙrC → ΗoEΟfO ⮌
252,554×5 nodes⮎ Νy0εVI → εuSΑZ2 → γYKΙv4 → ΨoMΗf8 → Οk8ΦjG ⮌
233,028×5 nodes⮎ ΑW2γxU → αWQΓx6 → ΤcQΓrC → ΗcEΟrO → ΑiEΟlU ⮌
2,162×(fixed) 1 node ⮎ kjζζjk ⮌
72 cycles12,103,890,210×(max) 19 nodes⮎ ΗiLζΘlO → ΙjNζΖkM → ΘlLζΘiN → ΙkOζΕjM → ΘkKζΙjN → ΚlNζΖiL → ΙmMζΗhM → ΘmOζΕhN → ΗjMζΗkO → ΘiMζΗlN → ΘkNζΖjN → ΗkLζΘjO → ΙjMζΗkM → ΘmMζΗhN → ΘkOζΕjN → ΗjKζΙkO → ΚkMζΗjL → ΙnMζΗgM → ΘmPζΔhN ⮌
1,730,522,850×(fixed) 1 node ⮎ ΘkMζΗjN ⮌
8+---Not showing digit sets 8+ due to verbosity.