Base 96: Cycles Sequences: Maximum Length Cycle Count

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)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
22 cycles24 nodes4ζ → 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 (fixed) 1 node lκm
41 cycle 18 nodesVκκΓ → ΓUΓW → YVΒΑ → WRΖΓ → eVΒu → WFΣΓ → ΓVΒW → XUΓΒ → YTΔΑ → aRΖy → eNΚu → mFΣm → ΒκκW → ΒVΒX → WTΔΓ → aVΒy → WNΚΓ → mVΒm
52 cycles2 nodesmkκmm → mκκκl
65 cycles126 nodesOH1θΡΛ → 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
72 cycles19 nodesΚkMκΛnP → ΜlOκΙmN → ΛnMκΛkO → ΜmPκΘlN → ΛmLκΜlO → ΝnOκΙkM → ΜoNκΚjN → ΛoPκΘjO → ΚlNκΚmP → ΛkNκΚnO → ΛmOκΙlO → ΚmMκΛlP → ΜlNκΚmN → ΛoNκΚjO → ΛmPκΘlO → ΚlLκΜmP → ΝmNκΚlM → ΜpNκΚiN → ΛoQκΗjO