Base 94: 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---
23 cycles3,348×(max) 36 nodes⮎ 0θ → η1 → ε3 → α7 → ΡF → ΑV → UΒ → Wz → SΔ → av → KΜ → qf → AΧ → ΛL → oh → 6β → ΤD → ΕR → ct → GΠ → yX → QΖ → er → CΥ → ΗP → gp → 8Ω → ΟH → wZ → MΚ → mj → 2ζ → γ5 → ΦB → ΙN → kl ⮌
837×9 nodes⮎ 4δ → Ψ9 → ΝJ → sd → EΣ → ΓT → Yx → OΘ → in ⮌
186×2 nodes⮎ IΞ → ub ⮌
31 cycle 142,786×(fixed) (max) 1 node ⮎ kθl ⮌
411 cycles318,663×(max) 23 nodes⮎ I9ΧΟ → ΝvZK → sLΚe → oDΣi → Ε5βS → ΦbtC → ΙHΞO → wjla → M1ζΛ → εnh4 → α5β8 → ΦΠFC → ΙzVO → kTΒm → Y1ζy → εPΖ4 → αfp8 → Ρ9ΧG → ΝzVK → sTΒe → YDΣy → ΕPΖS → gbtq ⮌
318,250×(max) 23 nodes⮎ YPΖy → gPΖq → g9Χq → Ν9ΧK → ΝrdK → sDΣe → ΕDΣS → ΕbtS → cHΞu → wHΞa → wLΚa → oLΚi → o5βi → Φ5βC → ΦΘNC → ΙjlO → k1ζm → ε1ζ4 → εΩ74 → αΠF8 → ΡzVG → ΑTΒW → YTΒy ⮌
317,007×(max) 23 nodes⮎ 61ζγ → εΥB4 → αΘN8 → ΡjlG → Α1ζW → εTΒ4 → αXx8 → ΡPΖG → ΑfpW → U9ΧΓ → ΝXxK → sPΖe → gDΣq → Ε9ΧS → ΝbtK → sHΞe → wDΣa → ΕLΚS → obti → I5βΟ → ΦvZC → ΙLΚO → ojli ⮌
315,250×(max) 23 nodes⮎ E5βΤ → ΦΔRC → ΙbtO → kHΞm → w1ζa → εLΚ4 → αnh8 → Ρ5βG → ΦzVC → ΙTΒO → kXxm → Q1ζΗ → εfp4 → α9Χ8 → ΡΜJG → ΑrdW → UDΣΓ → ΕXxS → cPΖu → gHΞq → w9Χa → ΝLΚK → snhe ⮌
315,084×(max) 23 nodes⮎ I1ζΟ → εvZ4 → αLΚ8 → ΡnhG → Α5βW → ΦTΒC → ΙXxO → kPΖm → g1ζq → ε9Χ4 → αΜJ8 → ΡrdG → ΑDΣW → ΕTΒS → cXxu → QHΞΗ → wfpa → M9ΧΛ → ΝnhK → s5βe → ΦDΣC → ΙΔRO → kbtm ⮌
313,962×(max) 23 nodes⮎ M5βΛ → ΦnhC → Ι5βO → ΦjlC → Ι1ζO → εjl4 → α1ζ8 → εΠF4 → αzV8 → ΡTΒG → ΑXxW → UPΖΓ → gXxq → Q9ΧΗ → ΝfpK → s9Χe → ΝDΣK → ΕrdS → cDΣu → ΕHΞS → wbta → MHΞΛ → wnha ⮌
313,850×(max) 23 nodes⮎ A1ζΨ → εΜJ4 → αrd8 → ΡDΣG → ΕzVS → cTΒu → YHΞy → wPΖa → gLΚq → o9Χi → Ν5βK → ΦrdC → ΙDΣO → ΕjlS → c1ζu → εHΞ4 → αvZ8 → ΡLΚG → ΑnhW → U5βΓ → ΦXxC → ΙPΖO → kfpm ⮌
313,812×(max) 23 nodes⮎ MDΣΛ → ΕnhS → c5βu → ΦHΞC → ΙvZO → kLΚm → o1ζi → ε5β4 → αΥB8 → ΡΘNG → ΑjlW → U1ζΓ → εXx4 → αPΖ8 → ΡfpG → Α9ΧW → ΝTΒK → sXxe → QDΣΗ → ΕfpS → c9Χu → ΝHΞK → wrda ⮌
313,718×(max) 23 nodes⮎ E1ζΤ → εΔR4 → αbt8 → ΡHΞG → ΑvZW → ULΚΓ → oXxi → Q5βΗ → ΦfpC → Ι9ΧO → ΝjlK → s1ζe → εDΣ4 → αΔR8 → ΡbtG → ΑHΞW → wTΒa → YLΚy → oPΖi → g5βq → Φ9ΧC → ΝΘNK → sjle ⮌
312,678×(max) 23 nodes⮎ E9ΧΤ → ΝΔRK → sbte → IDΣΟ → ΕvZS → cLΚu → oHΞi → w5βa → ΦLΚC → ΙnhO → k5βm → Φ1ζC → εΘN4 → αjl8 → Ρ1ζG → εzV4 → αTΒ8 → ΡXxG → ΑPΖW → gTΒq → Y9Χy → ΝPΖK → sfpe ⮌
312,472×(max) 23 nodes⮎ A5βΨ → ΦΜJC → ΙrdO → kDΣm → Ε1ζS → εbt4 → αHΞ8 → ΡvZG → ΑLΚW → oTΒi → Y5βy → ΦPΖC → ΙfpO → k9Χm → Ν1ζK → εrd4 → αDΣ8 → ΡΔRG → ΑbtW → UHΞΓ → wXxa → QLΚΗ → ofpi ⮌
53 cycles45,185,286×3 nodes⮎ ΑTθΒW → ΓUθΑU → ΒXθxV ⮌
22,716,556×(max) 4 nodes⮎ ΑUθΑW → ΒTθΒV → ΓVθzU → ΒWθyV ⮌
8,928×2 nodes⮎ ljθll → lθθθk ⮌
63 cycles770,343,951×(max) 53 nodes⮎ WTFΠΓΑ → ΑZTΒwW → YUMΙΒy → mXPΖyk → gR1ζΕq → εd9Χs4 → αΝEΡJ8 → ΡΓscTG → ΑZFΠwW → ΑUMΙΒW → mXTΒyk → YR1ζΕy → εdPΖs4 → αgEΡp8 → ΡΓ8ΨTG → ΟΑYwVI → wVNΘΑa → kVLΚΑm → oV1ζΑi → εV5βΑ4 → αΦUΑB8 → ΡΚVzMG → ΑnTΒiW → YU4γΒy → ΨXPΖyA → ΝgQΕpK → se8Ψre → ΟECΤΣI → ΗΔvZSQ → gbLΚuq → oJ9ΧΝi → Νt5βcK → ΦsGΟdC → ΙyEΡXO → ΓkQΕlU → eY0ηxs → ηPDΣΗ2 → εΕgoR4 → αd7Ωs8 → ΣΠEΡGF → ΔΒyWUT → aXRΔyw → cRLΚΕu → odHΞsi → wF5βΡa → ΦΒLΚUC → ΙoWyhO → kS6αΔm → Τb1ζuE → εΕIΝR4 → αucsb8 → ΡJFΠΝG → ΒzscWV ⮌
350,182,955×7 nodes⮎ mXDΣyk → ΕR1ζΕS → εdbts4 → αIEΡΞ8 → ΡΓuaTG → ΑZJΜwW → sUMΙΒe ⮌
2,256×(fixed) 1 node ⮎ lkθθkl ⮌
71 cycle 16,007,560,706×(max) 4 nodes⮎ ΙkLθΚlO → ΛlNθΘkM → ΚnMθΙiN → ΚmPθΖjN ⮌
8+---Not showing digit sets 8+ due to verbosity.