Base 68: Cycles Sequences: All Cycle Counts

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)		 Frequency Cycle
Length		 Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
23 cycles1,474×(max) 22 nodes⮎ 0Ζ → Ε1 → Γ3 → y7 → qF → aV → 4Β → w9 → mJ → Sd → Av → kL → Oh → In → Ub → 6z → sD → eR → Ct → gP → Gp → YX ⮌
737×11 nodes⮎ 2Δ → Α5 → uB → iN → Kl → Qf → Er → cT → 8x → oH → WZ ⮌
67×(fixed) 1 node ⮎ Mj ⮌
31 cycle 54,672×(fixed) (max) 1 node ⮎ XΖY ⮌
48 cycles177,015×(max) 4 nodes⮎ C3Βu → yhN8 → qJlG → aRdW ⮌
142,392×(max) 4 nodes⮎ K3Βm → yRd8 → qBtG → iZVO ⮌
136,472×(max) 4 nodes⮎ a3ΒW → y3Β8 → ypF8 → qZVG ⮌
133,948×(max) 4 nodes⮎ S3Βe → yBt8 → qhNG → aJlW ⮌
133,446×(max) 4 nodes⮎ SBte → iBtO → iJlO → SJle ⮌
105,888×(max) 4 nodes⮎ aBtW → i3ΒO → yJl8 → qRdG ⮌
89,478×2 nodes⮎ KBtm → iRdO ⮌
52,928×2 nodes⮎ q3ΒG → yZV8 ⮌
52 cycles13,986,786×(max) 4 nodes⮎ jLΖjN → kLΖjM → kNΖhM → jMΖiN ⮌
4,690×2 nodes⮎ YWΖYY → YΖΖΖX ⮌
63 cycles169,863,599×(max) 29 nodes⮎ K6ΖΖym → 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 ⮌
365,595×11 nodes⮎ ki0ΕNM → ΕOKkh2 → ΓQImf4 → yUEqb8 → qc6yTG → sa8wVE → oe4ΑRI → wWCsZA → mg2ΓPK → ΑSGod6 → uYAuXC ⮌
1,190×(fixed) 1 node ⮎ YXΖΖXY ⮌
72 cycles1,556,425,860×(max) 19 nodes⮎ oWFΖpZI → qXHΖnYG → pZFΖpWH → qYIΖmXG → pYEΖqXH → rZHΖnWF → qaGΖoVG → paIΖmVH → oXGΖoYI → pWGΖoZH → pYHΖnXH → oYFΖpXI → qXGΖoYG → paGΖoVH → pYIΖmXH → oXEΖqYI → rYGΖoXF → qbGΖoUG → paJΖlVH ⮌
243,153,136×(fixed) 1 node ⮎ pYGΖoXH ⮌
82 cycles11,197,987,475×(max) 104 nodes⮎ ULKEqlkc → 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 ⮌
5,673,066,182×83 nodes⮎ G751ΔΑyq → ΓvrZVEA4 → yld3ΒSK8 → yqRAueF8 → qkbCsULG → gaP6ygVQ → sHG4ΑpoE → weZWYWRA → mD31ΔΓsK → ΓzfRdQ64 → ytFBtqC8 → qihaUONG → aLJ5zmkW → uTP3ΒgcC → yiH8woN8 → qoXKkYHG → aXQ0ΕfYW → ΕF40ΕΒq2 → ΕΓxaU832 → Γzp5zG64 → yutYWCB8 → qjh1ΔOMG → ΓaNImiV4 → yUL4Αkb8 → wqP6ygFA → smbGoUJE → eYT6ycXS → sC90ΕwtE → ΕnhdROI2 → ΓVJBtma4 → yiT4ΑcN8 → wqL8wkFA → ombOgUJI → WTI6ynca → sV93ΒwaE → yne4ΑRI8 → wqVCsaFA → mgb4ΑUPK → wSH6yodA → smXAuYJE → keT0ΕcRM → ΕOD8wsh2 → ΓofImQH4 → yXUEqbY8 → qc70ΕyTG → Εra8wVE2 → Γod4ΑSH4 → ywXAuY98 → qnk0ΕLIG → ΕaVOgaV2 → ΓI54ΑΑn4 → ywvUaA98 → qnl5zKIG → uaVQeaVC → iE54ΑΑrO → wvdJlSAA → mlSAudKK → kSRAuedM → kODAushM → kfOImhQM → UOJEqmhc → cTJ7xmcU → qT97xwcG → qna8wVIG → oaV4ΑaVI → wW54ΑΑZA → wvm2ΓJAA → ΑmlScKJ6 → uTR9vecC → miD8wsNK → ofSKkdQI → WQFAuqfa → kbF3ΒqUM → ybO6yhU8 → sqJ6ymFE → sebScURE → eDA6yvsS → slfBtQKE → ieREqeRO → cKDCsslU → gfR7xeQQ → qGFCsqpG → gbaYWVUQ ⮌
9+---Not showing digit sets 9+ due to verbosity.