Base 96: 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---
22 cycles2,280×(max) 24 nodes⮎ 0κ → ι1 → η3 → γ7 → ΤF → ΓV → WΒ → UΔ → Yz → QΘ → gr → AΩ → ΝL → qh → 8β → ΡH → yZ → OΚ → kn → 2θ → ε5 → ΨB → ΛN → ml ⮌
2,280×(max) 24 nodes⮎ 4ζ → α9 → ΟJ → ud → GΣ → ΑX → SΖ → cv → IΠ → wb → KΞ → sf → CΧ → ΙP → ip → 6δ → ΦD → ΗR → et → EΥ → ΕT → ax → MΜ → oj ⮌
31 cycle 152,000×(fixed) (max) 1 node ⮎ lκm ⮌
41 cycle 3,764,280×(max) 18 nodes⮎ VκκΓ → ΓUΓW → YVΒΑ → WRΖΓ → eVΒu → WFΣΓ → ΓVΒW → XUΓΒ → YTΔΑ → aRΖy → eNΚu → mFΣm → ΒκκW → ΒVΒX → WTΔΓ → aVΒy → WNΚΓ → mVΒm ⮌
52 cycles75,278,114×(fixed) 1 node ⮎ ΓVκΒW ⮌
9,310×(max) 2 nodes⮎ mkκmm → mκκκl ⮌
65 cycles1,097,865,093×(max) 126 nodes⮎ OH1θΡΛ → ηzllY4 → γQκκΗ8 → βΘJΞQ9 → ΡugqdI → yH9ΩΡa → ΟzNΚYK → umQΗle → gG0ιΣs → ιΒBΧW2 → ηΛUΓN4 → γnXzk8 → ΤS2ηΖG → εΓcuV6 → ΨXHΠΑC → ΛySΕZO → mcOΙvm → kIκκΟo → ΠnPΘkJ → wi2ηpc → εK6γΞ6 → ΨΦseDC → ΛΘDΥQO → ΗmgqlS → eA0ιΩu → ιΞFΣK2 → ηΓseV4 → γXDΥΑ8 → ΤΗSΕRG → ΓfbvsW → WKCΦΞΓ → ΙtVΒeQ → iWEΤΒq → ΕV7βΓU → ΤaWΑxG → ΓUMΛΔW → oZVΒyk → WP3ζΙΓ → γjVΒo8 → ΤW4εΒG → αΓUΓVA → ΟYWΑzK → uUQΗΔe → gZFΣys → ΓPBΧΙW → ΛjVΒoO → mW4εΒm → αUκκΓA → ΩΔLΜUB → ΝqYyhM → qQ8αΘi → Ρh7βqI → Τy8αZG → ΡΓOΙVI → ykWΑna → UO2ηΚΕ → εlZxm6 → ΨO0ιΚC → ιΛkmN2 → ηn1θk4 → ηγ2η74 → εγΤE76 → ΨΥΔTEC → ΛΖZxSO → mdNΚum → mGκκΡm → ΣlTΔmH → Αa0ιxY → ιSMΛΖ2 → ηocuj4 → γI4εΠ8 → αΤwaFA → ΟΔLΜUK → uqYyhe → QG8αΣΙ → ΡΒhpWI → yV7βΓa → ΤXNΚΑG → ΓmSΕlW → cW0ιΒw → ιVJΞΓ2 → ηuWΑd4 → γUGΡΔ8 → ΤΑYyXG → ΓTPΘΕW → ibVΒwq → WL7βΝΓ → ΤrVΒgG → ΓWAΨΒW → ΝWUΓΒM → qYUΓzi → YR7βΗΑ → ΤfRΖsG → ΓeCΦtW → ΙWEΤΒQ → ΕiUΓpU → aY6γzy → ΦRNΚΗE → ΗmeslS → eE0ιΥu → ιΖFΣS2 → ηΓcuV4 → γXHΠΑ8 → ΤySΕZG → ΓcOΙvW → kWIΟΒo → wV3ζΓc → γXJΞΑ8 → ΤuSΕdG → ΓcGΡvW → ΑWIΟΒY → wVRΖΓc → eXJΞΑu → uTFΣΕe → ΓbFΣwW → ΓWKΝΒW → sWUΓΒg → YVBΧΓΑ → ΛXRΖΑO → meSΕtm → cEκκΤw → ΥvLΜcF → ΕqIΟhU → wa8αxc → ΡNJΞΛI → yumkda ⮌
138,207,071×45 nodes⮎ UIκκΟΕ → ΠΔ9ΩUJ → ΟwYybK → uQKΝΘe → shFΣqg → ΓC8αΧW → ΡΚVΒOI → ylVΒma → WO0ιΚΓ → ιlVΒm2 → ηW0ιΒ4 → ιγUΓ72 → ηΥXzE4 → γΖRΖS8 → ΤecutG → ΓIEΤΠW → ΕxVΒaU → aWMΛΒy → oVNΚΓk → mX3ζΑm → γSκκΕ8 → βΖLΜS9 → ΡqcuhI → yI8αΠa → ΡxNΚaI → ymMΛla → oO0ιΚk → ιl3ζm2 → ηγ0ι74 → ιγΤE72 → ηΥΔTE4 → γΖZxS8 → ΤdNΚuG → ΓmGΡlW → ΑW0ιΒY → ιVRΖΓ2 → ηeWΑt4 → γUEΤΔ8 → ΤΕYyTG → ΓbPΘwW → iWKΝΒq → sV7βΓg → ΤXBΧΑG → ΛΓSΕVO → mcWΑvm ⮌
25,836,602×3 nodes⮎ cVFΣΓw → ΓXJΞΑW → uWSΕΒe ⮌
5,428,706×2 nodes⮎ WSGΡΖΓ → ΑdVΒuY ⮌
2,352×(fixed) 1 node ⮎ mlκκlm ⮌
72 cycles16,206,521,746×(max) 19 nodes⮎ ΚkMκΛnP → ΜlOκΙmN → ΛnMκΛkO → ΜmPκΘlN → ΛmLκΜlO → ΝnOκΙkM → ΜoNκΚjN → ΛoPκΘjO → ΚlNκΚmP → ΛkNκΚnO → ΛmOκΙlO → ΚmMκΛlP → ΜlNκΚmN → ΛoNκΚjO → ΛmPκΘlO → ΚlLκΜmP → ΝmNκΚlM → ΜpNκΚiN → ΛoQκΗjO ⮌
2,260,431,278×(fixed) 1 node ⮎ ΛmNκΚlO ⮌
8+---Not showing digit sets 8+ due to verbosity.