Base 74: 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---
25 cycles1,460×(max) 20 nodes⮎ 0Μ → Λ1 → Ι3 → Ε7 → wF → gV → AΒ → qL → Uh → Cz → mP → Mp → Sj → Gv → eX → 6Ζ → yD → kR → It → ab ⮌
730×10 nodes⮎ 2Κ → Η5 → ΑB → oN → Ql → Kr → Wf → 8Δ → uH → cZ ⮌
292×4 nodes⮎ 4Θ → Γ9 → sJ → Yd ⮌
146×2 nodes⮎ Ex → iT ⮌
73×(fixed) 1 node ⮎ On ⮌
31 cycle 70,226×(fixed) (max) 1 node ⮎ aΜb ⮌
49 cycles162,437×(max) 18 nodes⮎ E5Ζy → ΑjRC → oHtO → cPla → M1Κq → ΙTh4 → ΕDx8 → wjRG → gHtW → c9Βa → s1ΚK → ΙXd4 → Ε5Ζ8 → ΑvFC → ofVO → Q9Βm → sLpK → YThe ⮌
162,236×(max) 18 nodes⮎ QLpm → ULpi → UDxi → kDxS → kHtS → cHta → c1Κa → Ι1Κ4 → ΙΔ74 → ΕvF8 → wfVG → g9ΒW → s9ΒK → sXdK → Y5Ζe → Α5ΖC → ΑnNC → oPlO ⮌
160,222×(max) 18 nodes⮎ A1ΚΓ → ΙrJ4 → ΕXd8 → w5ΖG → ΑfVC → o9ΒO → sPlK → YLpe → U5Ζi → ΑDxC → ojRO → QHtm → cLpa → U1Κi → ΙDx4 → ΕjR8 → wHtG → gbZW ⮌
159,746×(max) 18 nodes⮎ A5ΖΓ → ΑrJC → oXdO → Q5Ζm → ΑLpC → oThO → QDxm → kLpS → UHti → cDxa → k1ΚS → ΙHt4 → ΕbZ8 → w1ΚG → ΙfV4 → Ε9Β8 → wrJG → gXdW ⮌
158,899×(max) 18 nodes⮎ 61ΚΗ → ΙzB4 → ΕnN8 → wPlG → gLpW → U9Βi → sDxK → kXdS → I5Ζu → ΑbZC → o1ΚO → ΙPl4 → ΕLp8 → wThG → gDxW → k9ΒS → sHtK → cXda ⮌
158,142×(max) 18 nodes⮎ I1Κu → ΙbZ4 → Ε1Κ8 → ΙvF4 → ΕfV8 → w9ΒG → sfVK → Y9Βe → s5ΖK → ΑXdC → o5ΖO → ΑPlC → oLpO → UPli → MDxq → kThS → IDxu → kbZS ⮌
157,850×(max) 18 nodes⮎ I9Βu → sbZK → Y1Κe → Ι5Ζ4 → ΕzB8 → wnNG → gPlW → M9Βq → sThK → YDxe → k5ΖS → ΑHtC → obZO → Q1Κm → ΙLp4 → ΕTh8 → wDxG → kfVS ⮌
156,106×(max) 18 nodes⮎ E1Κy → ΙjR4 → ΕHt8 → wbZG → g1ΚW → Ι9Β4 → ΕrJ8 → wXdG → g5ΖW → Α9ΒC → snNK → YPle → M5Ζq → ΑThC → oDxO → kPlS → MHtq → cTha ⮌
77,563×9 nodes⮎ E9Βy → sjRK → YHte → c5Ζa → Α1ΚC → ΙnN4 → ΕPl8 → wLpG → gThW ⮌
52 cycles21,105,468×(max) 4 nodes⮎ nNΜnP → oNΜnO → oPΜlO → nOΜmP ⮌
5,548×2 nodes⮎ bZΜbb → bΜΜΜa ⮌
65 cycles277,445,662×(max) 49 nodes⮎ A73ΘΕΓ → ΕxrJE8 → wjXdSG → gH5ΖuW → Αd9ΒYC → so4ΗNK → ΓYQkdA → sK4ΗrK → ΓYWedA → s84ΗΔK → ΓvXdGA → sf5ΖWK → ΑY8ΓdC → uo4ΗNI → ΓcQkZA → sK2ΙrK → ΗYWed6 → Α84ΗΔC → ΓvnNGA → sfPlWK → YM8Γpe → uT5ΖiI → ΑcEwZC → oi2ΙTO → ΗQEwl6 → ΑiKqTC → oWEwfO → iQ8ΓlU → uLDxqI → kcUgZS → IC2Ιzu → ΗnbZO6 → ΑP1ΚmC → ΙoMoN4 → ΕSQkj8 → wKGurG → geWeXW → A86ΕΔΓ → yvrJGE → kfXdWS → I95ΖΓu → ΑtbZIC → ob1ΚaO → ΙQ0Λl4 → ΛΕKq72 → ΙxVfE4 → Εj9ΒS8 → wsGuJG → geYcXW ⮌
409,193×10 nodes⮎ om0ΛPO → ΛQMol2 → ΙSKqj4 → ΕWGuf8 → we8ΓXG → ug6ΕVI → ycAΑZE → qk2ΙRM → ΗUIsh6 → ΑaCybC ⮌
59,000×2 nodes⮎ si4ΗTK → ΓYEwdA ⮌
47,350×2 nodes⮎ sO4ΗnK → ΓYOmdA ⮌
1,406×(fixed) 1 node ⮎ baΜΜab ⮌
71 cycle 3,176,716,326×(max) 4 nodes⮎ taGΜubJ → vbIΜsaH → udHΜtYI → ucKΜqZI ⮌
8+---Not showing digit sets 8+ due to verbosity.