Base 82: 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---
21 cycle 3,321×(max) 41 nodes⮎ 0Υ → 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 95,202×(fixed) (max) 1 node ⮎ eΥf ⮌
420 cycles118,173×(max) 10 nodes⮎ 61ΣΟ → ΡΘB4 → ΝvN8 → ΕXlG → oDΖW → sHΒS → kPta → U9Κq → ΑLxK → gbhe ⮌
116,622×(max) 10 nodes⮎ IDΖΓ → sjZS → Q9Κu → ΑTpK → gLxe → c1Σi → Ρ5Ξ4 → ΝΘB8 → ΕvNG → oXlW ⮌
115,174×(max) 10 nodes⮎ E5ΞΗ → ΙrRC → wPtO → YTpm → MDΖy → sbhS → Q5Ξu → ΙTpC → wLxO → cXli ⮌
114,242×(max) 10 nodes⮎ A5ΞΛ → ΙzJC → wfdO → Y1Σm → ΡDΖ4 → ΝrR8 → ΕPtG → oTpW → MHΒy → kbha ⮌
109,806×(max) 10 nodes⮎ M1Σy → Ρbh4 → Ν5Ξ8 → ΙΔFC → wnVO → YHΒm → kDΖa → s9ΚS → ΑPtK → gTpe ⮌
109,545×(max) 10 nodes⮎ g1Σe → Ρ1Σ4 → ΡΜ74 → ΝΔF8 → ΕnVG → oHΒW → kHΒa → k9Κa → Α9ΚK → ΑfdK ⮌
107,409×(max) 10 nodes⮎ M5Ξy → ΙbhC → w5ΞO → ΙXlC → wDΖO → sXlS → QDΖu → sTpS → QLxu → cTpi ⮌
107,245×(max) 10 nodes⮎ I9ΚΓ → ΑjZK → g9Κe → Α1ΣK → Ρfd4 → Ν1Σ8 → ΡΔF4 → ΝnV8 → ΕHΒG → ojZW ⮌
107,209×(max) 10 nodes⮎ U5Ξq → ΙLxC → wbhO → Y5Ξm → ΙDΖC → wrRO → YPtm → UDΖq → sLxS → cPti ⮌
105,017×(max) 10 nodes⮎ M9Κy → ΑbhK → g5Ξe → Ι1ΣC → ΡvN4 → ΝXl8 → ΕDΖG → snVS → QHΒu → kTpa ⮌
104,975×(max) 10 nodes⮎ E1ΣΗ → ΡrR4 → ΝPt8 → ΕTpG → oLxW → cHΒi → k5Ξa → Ι9ΚC → ΑvNK → gXle ⮌
104,919×(max) 10 nodes⮎ A1ΣΛ → ΡzJ4 → Νfd8 → Ε1ΣG → ΡnV4 → ΝHΒ8 → ΕjZG → o9ΚW → ΑHΒK → kfda ⮌
104,751×(max) 10 nodes⮎ ULxq → cLxi → c5Ξi → Ι5ΞC → ΙvNC → wXlO → YDΖm → sDΖS → sPtS → UPtq ⮌
104,087×(max) 10 nodes⮎ E9ΚΗ → ΑrRK → gPte → U1Σq → ΡLx4 → Νbh8 → Ε5ΞG → ΙnVC → wHΒO → kXla ⮌
97,172×(max) 10 nodes⮎ UHΒq → kLxa → c9Κi → Α5ΞK → ΙfdC → w1ΣO → ΡXl4 → ΝDΖ8 → ΕrRG → oPtW ⮌
97,172×(max) 10 nodes⮎ Q1Σu → ΡTp4 → ΝLx8 → ΕbhG → o5ΞW → ΙHΒC → wjZO → Y9Κm → ΑDΖK → sfdS ⮌
97,172×(max) 10 nodes⮎ I5ΞΓ → ΙjZC → w9ΚO → ΑXlK → gDΖe → s1ΣS → ΡPt4 → ΝTp8 → ΕLxG → obhW ⮌
97,108×(max) 10 nodes⮎ gHΒe → k1Σa → Ρ9Κ4 → ΝzJ8 → ΕfdG → o1ΣW → ΡHΒ4 → ΝjZ8 → Ε9ΚG → ΑnVK ⮌
58,287×5 nodes⮎ I1ΣΓ → ΡjZ4 → Ν9Κ8 → ΕzJG → ofdW ⮌
48,618×5 nodes⮎ YLxm → cDΖi → s5ΞS → ΙPtC → wTpO ⮌
53 cycles23,132,648×3 nodes⮎ sPΥtS → uQΥsQ → tTΥpR ⮌
11,686,768×(max) 4 nodes⮎ sQΥsS → tPΥtR → uRΥrQ → tSΥqR ⮌
6,804×2 nodes⮎ fdΥff → fΥΥΥe ⮌
67 cycles328,286,109×(max) 92 nodes⮎ IC0ΤΘΓ → 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 ⮌
136,525,492×43 nodes⮎ E82ΡΜΗ → ΟΔrRG6 → ΙnPtWC → wUGΓpO → mYKylY → eECΗΖg → ur1ΣSQ → ΡUOup4 → ΝWKyn8 → ΕeGΓfG → om0ΤXW → ΤIEΕΒ2 → ΡqiaT4 → ΝN7Μw8 → ΖΔYkGF → qnBΘWU → wMGΓxO → mbXliY → FD6ΝΗΖ → ΗtpTQE → sTLxqS → cQMwti → aT5Ξqk → ΙN9ΚwC → ΑwYkNK → gZBΘke → wB1ΣΙO → ΡxXlM4 → ΝbDΖi8 → Εs6ΝRG → ΗoQsVE → sSIΑrS → iQOutc → WT5Ξqo → ΙNHΒwC → wkYkZO → YCAΙΘm → yvDΖOM → scWmhS → QG4ΟΔu → ΛnTpWA → ΑMGΓxK → mgaidY ⮌
24,608,016×45 nodes⮎ IE0ΤΖΓ → ΤrjZS2 → ΡP9Κu4 → ΝΑUoJ8 → ΕhJzcG → og4ΟdW → ΛI2ΡΒA → ΟΑiaJ6 → Ιh7ΜcC → Εw4ΟNG → ΛoYkVA → ΑJBΘΑK → whfdcO → Y51ΣΟm → ΡΚDΖA4 → ΝzrRK8 → ΕfPteG → oU0ΤpW → ΤLHΒy2 → ΡkcgZ4 → ΝB3ΠΙ8 → ΝΕwMF8 → ΕpZjUG → oL9ΚyW → ΑdHΒgK → kg2Ρda → ΟA2ΡΚ6 → ΟΙyKB6 → ΙxdfMC → wb1ΣiO → ΡY6Νl4 → ΝΗCΗD8 → ΕusQPG → oVRroW → QJHΒΑu → khTpca → MA4ΟΚy → ΛzbhKA → Αf5ΞeK → Ιg0ΤdC → Τw2ΡN2 → ΡΟYk54 → ΝΚBΘA8 → ΕzvNKG → ofXleW ⮌
13,383,522×10 nodes⮎ I51ΣΟΓ → ΡΚjZA4 → Νz9ΚK8 → ΕΑeeJG → ogΥΥcW → nh7ΜcX → ΕG4ΟΔG → ΛomWVA → ΑJFΔΑK → ohfdcW ⮌
1,356,423×8 nodes⮎ oZ3ΠkW → ΝIAΙΒ8 → ΕyiaLG → od7ΜgW → ΕI2ΡΒG → ΟoiaV6 → ΙJ7ΜΑC → ΕwgcNG ⮌
820,013×2 nodes⮎ ΕJ3ΠΑG → ΝogcV8 ⮌
1,722×(fixed) 1 node ⮎ feΥΥef ⮌
71 cycle 6,348,337,254×(max) 4 nodes⮎ zeIΥΑfL → ΒfKΥyeJ → ΑhJΥzcK → ΑgMΥwdK ⮌
8+---Not showing digit sets 8+ due to verbosity.