Base 68: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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--
23 cycles22 nodes0Ζ → Ε1 → Γ3 → y7 → qF → aV → 4Β → w9 → mJ → Sd → Av → kL → Oh → In → Ub → 6z → sD → eR → Ct → gP → Gp → YX
31 cycle (fixed) 1 node XΖY
48 cycles4 nodesaBtW → i3ΒO → yJl8 → qRdG
52 cycles4 nodesjLΖjN → kLΖjM → kNΖhM → jMΖiN
63 cycles29 nodesK6ΖΖym → zlBtK7 → siQeNE → eLDrkS → ePBtgS → iHBtoO → iXJlYO → SK0Εle → ΕRBte2 → ΓiCsN4 → ygKkP8 → qQGofG → aYEqXW → c40ΕΒU → Εx7x82 → ΓqoGF4 → ybXXU8 → q6ΖΖyG → zp7xG7 → sqYWFE → eb1ΔUS → ΓC6yt4 → ysgOD8 → qfHnQG → aWEqZW → c42ΓΒU → Αx7x86 → uqoGFC → ibXXUO
72 cycles19 nodesoWFΖpZI → qXHΖnYG → pZFΖpWH → qYIΖmXG → pYEΖqXH → rZHΖnWF → qaGΖoVG → paIΖmVH → oXGΖoYI → pWGΖoZH → pYHΖnXH → oYFΖpXI → qXGΖoYG → paGΖoVH → pYIΖmXH → oXEΖqYI → rYGΖoXF → qbGΖoUG → paJΖlVH
82 cycles104 nodesULKEqlkc → cRP7xgeU → qHD7xsoG → qfaWYVQG → aF51ΔΑqW → Γvb3ΒUA4 → zxl6yK87 → trpQeGED → gdZDrWSQ → eGB2ΓupS → ΑjZBtWM6 → uiN2ΓiNC → ΑiLKkkN6 → uQPKkgfC → iQHEqofO → cXKEqlYU → cR80ΕxeU → ΕpD7xsG2 → ΓqfYWQF4 → ybF1ΔqU8 → Γqb6yUF4 → ysb6yUD8 → sqf6yQFE → sebEqURE → ecD6ysTS → sfC8wtQE → oheEqROI → cWJCsmZU → gT82ΓxcQ → ΑpG8wpG6 → uoZYWWHC → iX31ΔΓYO → ΓzK0Εl64 → ΕytQeC72 → ΓrhDrOE4 → yedImSR8 → qUDAusbG → kfa6yVQM → sOF4ΑqhE → webImURA → mUD6ysbK → sfS6ydQE → seFAuqRE → kebCsURM → gOD6yshQ → sfJFpmQE → eaTEqcVS → cC94ΑwtU → wnh7xOIA → qmVImaJG → aUT4ΑcbW → w973ΒywA → yrnlJIE8 → qdVRdaSG → aCB4ΑutW → wjh3ΒOMA → ymNImiJ8 → qUTKkcbG → aQ96ywfW → snF3ΒqIE → yebUaUR8 → qD75zysG → urfZVQEC → idF3ΒqSO → ybKAulU8 → qkR6yeLG → saPCsgVE → geH4ΑoRQ → wXGCspYA → mgZ0ΕWPK → ΕSH2Γod2 → ΓΑXAuY54 → yvk0ΕLA8 → ΕqlOgKF2 → ΓbRHneU4 → yWD6ysZ8 → sqf2ΓQFE → ΑebEqUR6 → ucD6ysTC → sif8wQNE → oeLEqkRI → cWPCsgZU → gH82ΓxoQ → ΑpXFpYG6 → uaZ0ΕWVC → Εi52ΓΑN2 → ΓΑvKkA54 → yvlPfKA8 → qlRFpeKG → bZRCseWV → gD62ΓzsQ → ΑtfFpQC6 → uhaEqVOC → icJ4ΑmTO → wTK8wlcA → omR8weJI → oWTCscZI → gW92ΓwZQ → ΑnG2ΓpI6 → ΑuZUaWB6 → uj62ΓzMC → ΑtiMiNC6 → uhMKkjOC → iQNImifO