Base 82: 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--
21 cycle 41 nodes0Υ → Τ1 → Ρ3 → Ν7 → ΕF → oV → IΒ → ib → 6Ξ → ΗD → sR → Qt → Sr → Ov → Wn → GΔ → mX → EΖ → qT → Mx → aj → 8Μ → ΓH → kZ → AΚ → yL → ch → 4Π → Λ9 → ΑJ → gd → 2Σ → Ο5 → ΙB → wN → Yl → CΘ → uP → Up → Kz → ef
31 cycle (fixed) 1 node eΥf
420 cycles10 nodesgHΒe → k1Σa → Ρ9Κ4 → ΝzJ8 → ΕfdG → o1ΣW → ΡHΒ4 → ΝjZ8 → Ε9ΚG → ΑnVK
53 cycles4 nodessQΥsS → tPΥtR → uRΥrQ → tSΥqR
67 cycles92 nodesIC0ΤΘΓ → ΤvjZO2 → ΡX9Κm4 → ΝΑEΕJ8 → ΕqgcTG → oN3ΠwW → ΝZHΒk8 → ΕkAΙZG → yoAΙVM → ycIΑhM → ic4Οhc → Λ64ΟΞA → ΛΘzJCA → ΑvfdOK → gX1Σme → ΡF1ΣΕ4 → ΡΝoU74 → ΝΖJzE8 → ΕrfdSG → oP1ΣuW → ΡVHΒo4 → ΝkIΑZ8 → ΕiAΙbG → yo6ΝVM → ΗcIΑhE → si4ΟbS → ΛQ6ΝtA → ΗΑSqJE → shNvcS → YQ4Οtm → ΛTDΖqA → ΑsMwRK → gaQsje → S91ΣΛs → ΡΒPtI4 → ΝjTpa8 → ΕM8ΛxG → ΓoaiVI → kJ7ΜΑa → Εh9ΚcG → Αo4ΟVK → ΛgIΑdA → Αi2ΡbK → Οg6Νd6 → ΙΗ2ΡDC → ΟwsQN6 → ΙZRrkC → wQAΙtO → yYSqlM → cOCΗvi → uX5ΞmQ → ΙUEΕpC → wqKyTO → eYMwlg → aD1ΣΗk → Ρt9ΚQ4 → ΝΑSqJ8 → ΕhNvcG → oY4ΟlW → ΛICΗΒA → ΑuiaPK → gV7Μoe → ΕJ1ΣΑG → ΡogcV4 → ΝJ3ΠΑ8 → ΝΕgcF8 → Εp3ΠUG → ΝoKyV8 → ΕeIΑfG → oi0ΤbW → ΤI6ΝΒ2 → ΡΗiaD4 → Νt7ΜQ8 → ΖΔSqGF → qnNvWU → YMGΓxm → mbDΖiY → sE6ΝΖS → ΗrPtSE → sUOupS → WQKyto → eTHΒqg → kN1Σwa → ΡZ9Κk4 → ΝΑAΙJ8 → ΕygcLG → od3ΠgW → ΝI2ΡΒ8 → ΟΕiaF6 → Ιp7ΜUC → ΕwKyNG → oeYkfW
71 cycle 4 nodeszeIΥΑfL → ΒfKΥyeJ → ΑhJΥzcK → ΑgMΥwdK