Base 90: 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---
25 cycles1,068×(max) 12 nodes⮎ 0δ → γ1 → α3 → Φ7 → ΝF → wV → QΒ → ar → GΜ → uX → MΖ → ij ⮌
1,068×(max) 12 nodes⮎ 2β → Ψ5 → ΡB → ΕN → gl → 4Ω → Τ9 → ΙJ → od → AΣ → ΗL → kh ⮌
1,068×(max) 12 nodes⮎ 8Υ → ΛH → sZ → IΚ → qb → EΞ → yT → Ux → Sz → Wv → OΔ → en ⮌
534×6 nodes⮎ 6Χ → ΟD → ΑR → Yt → KΘ → mf ⮌
267×3 nodes⮎ CΠ → ΓP → cp ⮌
31 cycle 125,490×(fixed) (max) 1 node ⮎ iδj ⮌
427 cycles168,305×(max) 12 nodes⮎ M5ΧΗ → ΡjhC → Ε1βO → αfl4 → Φ5Χ8 → ΡΜFC → ΕvVO → gPΒm → c5Χq → ΡDΞC → ΕzRO → gXtm ⮌
165,510×(max) 12 nodes⮎ IDΞΛ → ΑrZS → YHΚu → sLΖa → kHΚi → s1βa → αHΚ4 → ΦrZ8 → ΝHΚG → wrZW → QHΚΓ → sbpa ⮌
163,495×(max) 12 nodes⮎ 61βΨ → αΠB4 → ΦΔN8 → ΝflG → w5ΧW → ΡPΒC → ΕbpO → gDΞm → Α5ΧS → ΡXtC → ΕLΖO → kfli ⮌
162,634×(max) 12 nodes⮎ U1βy → αTx4 → ΦTx8 → ΝTxG → wTxW → UPΒy → cTxq → UDΞy → ΑTxS → YTxu → ULΖy → kTxi ⮌
162,400×(max) 12 nodes⮎ A5ΧΤ → ΡΘJC → ΕndO → g9Σm → Ι5ΧK → ΡndC → Ε9ΣO → ΙflK → o5Χe → Ρ9ΣC → ΙΔNK → ofle ⮌
153,173×(max) 12 nodes⮎ Q9ΣΓ → ΙbpK → oDΞe → Α9ΣS → ΙXtK → oLΖe → k9Σi → Ι1βK → αnd4 → Φ9Σ8 → ΝΘJG → wndW ⮌
153,073×(max) 12 nodes⮎ YPΒu → cLΖq → kDΞi → Α1βS → αXt4 → ΦLΖ8 → ΝjhG → w1βW → αPΒ4 → Φbp8 → ΝDΞG → ΑvVS ⮌
152,151×(max) 12 nodes⮎ YLΖu → kLΖi → k1βi → α1β4 → αΥ74 → ΦΜF8 → ΝvVG → wPΒW → cPΒq → cDΞq → ΑDΞS → ΑXtS ⮌
151,205×(max) 12 nodes⮎ E5ΧΟ → ΡzRC → ΕXtO → gLΖm → k5Χi → Ρ1βC → αΔN4 → Φfl8 → Ν5ΧG → ΡvVC → ΕPΒO → gbpm ⮌
150,691×(max) 12 nodes⮎ MDΞΗ → ΑjhS → Y1βu → αLΖ4 → Φjh8 → Ν1βG → αvV4 → ΦPΒ8 → ΝbpG → wDΞW → ΑPΒS → cXtq ⮌
150,165×(max) 12 nodes⮎ Q5ΧΓ → ΡbpC → ΕDΞO → ΑflS → Y5Χu → ΡLΖC → ΕjhO → g1βm → α5Χ4 → ΦΠB8 → ΝΔNG → wflW ⮌
149,525×(max) 12 nodes⮎ A1βΤ → αΘJ4 → Φnd8 → Ν9ΣG → ΙvVK → oPΒe → c9Σq → ΙDΞK → ΑndS → Y9Σu → ΙLΖK → ojhe ⮌
149,449×(max) 12 nodes⮎ E1βΟ → αzR4 → ΦXt8 → ΝLΖG → wjhW → Q1βΓ → αbp4 → ΦDΞ8 → ΝzRG → wXtW → QLΖΓ → kbpi ⮌
147,611×(max) 12 nodes⮎ I1βΛ → αrZ4 → ΦHΚ8 → ΝrZG → wHΚW → sPΒa → cHΚq → sDΞa → ΑHΚS → sXta → MHΚΗ → sjha ⮌
145,505×(max) 12 nodes⮎ E9ΣΟ → ΙzRK → oXte → M9ΣΗ → ΙjhK → o1βe → α9Σ4 → ΦΘJ8 → ΝndG → w9ΣW → ΙPΒK → obpe ⮌
134,880×(max) 12 nodes⮎ M1βΗ → αjh4 → Φ1β8 → αΜF4 → ΦvV8 → ΝPΒG → wbpW → QDΞΓ → ΑbpS → YDΞu → ΑLΖS → kXti ⮌
80,095×6 nodes⮎ I9ΣΛ → ΙrZK → oHΚe → s9Σa → ΙHΚK → snda ⮌
69,576×6 nodes⮎ c1βq → αDΞ4 → ΦzR8 → ΝXtG → wLΖW → kPΒi ⮌
46,560×4 nodes⮎ gHΚm → s5Χa → ΡHΚC → ΕrZO ⮌
45,864×4 nodes⮎ U5Χy → ΡTxC → ΕTxO → gTxm ⮌
45,816×4 nodes⮎ g5Χm → Ρ5ΧC → ΡΔNC → ΕflO ⮌
44,424×4 nodes⮎ I5ΧΛ → ΡrZC → ΕHΚO → sfla ⮌
35,330×3 nodes⮎ o9Σe → Ι9ΣK → ΙndK ⮌
34,170×3 nodes⮎ U9Σy → ΙTxK → oTxe ⮌
23,976×2 nodes⮎ Ε5ΧO → ΡflC ⮌
22,236×2 nodes⮎ UHΚy → sTxa ⮌
11,826×(fixed) 1 node ⮎ sHΚa ⮌
52 cycles54,882,740×(fixed) 1 node ⮎ yTδxU ⮌
8,188×(max) 2 nodes⮎ jhδjj → jδδδi ⮌
66 cycles858,769,162×(max) 247 nodes⮎ KIGΛΚΙ → urndaY → MH9ΣΛΗ → ΙtjhYK → oL1βΗe → αl9Σg4 → ΦΙ4ΨJ8 → ΤΝocFA → ΙxBΠUK → ΕoSydO → gWAΡvm → ΗP5ΧΓM → ΡkcohC → ΕC2αΠO → ΨΔflO6 → Ρf5ΧmC → ΡΕ6ΦNC → ΟΕgkNE → Αh3ΩkS → ΦY2αt8 → ΨΝKΗF6 → ΡxlfUC → ΕT5ΧyO → ΡgUwlC → ΕS4ΨzO → ΤgWulA → ΙO4ΨΔK → ΤoemdA → ΙB7ΥΡK → ΝΖndMG → wj9ΣiW → ΙQ0γΒK → γoaqd2 → αGAΡΜ4 → ΦΗuWL8 → ΝlNΔgG → wg4ΨlW → ΤQ4ΨΒA → ΤΙaqJA → ΙpFΜcK → woCΟdW → ΓQAΡΒQ → ΗcaqpM → kGCΟΜi → Γv1βWQ → αcOΓp4 → ΦeCΟn8 → ΝΓ8ΤPG → ΛwcoVI → sRBΠΑa → ΕZHΚsO → sgIΙla → qI4ΨΚc → ΤrDΞaA → ΙΑGΛRK → uoYsdY → MKAΡΘΗ → ΗnjheM → k91βΤi → αΚ1βI4 → αΦqa74 → ΦΞFΜE8 → ΝzvVSG → wXPΒuW → cQMΕΒq → ibDΞqk → ΑF1βΝS → αxXtU4 → ΦTLΖy8 → ΝkUwhG → wS2αzW → ΨXPΒu6 → ΡcMΕpC → ΕiCΟjO → Γg0γlQ → γc4Ψp2 → αΤCΟ94 → ΦΚΒPI8 → ΝrbpaG → wHDΞΛW → ΑtPΒYS → cYKΗtq → mLDΞΗg → Αl5ΧgS → ΡY4ΨtC → ΤΕKΗNA → ΙmgkfK → o73ΩΦe → ΦΞ9ΣE8 → ΝΙySJG → wpVvcW → RPCΟΓΒ → ΓdZroQ → cIAΡΚq → ΗrDΞaM → ΑkGΛhS → uY2αtY → ΨMKΗΖ6 → ΡmiifC → Ε6δδΦO → ΧΔFΜO7 → ΟwemVE → ΑR7ΥΑS → ΝZXtsG → wMIΙΖW → qjPΒic → cE0γΞq → γzDΞS2 → αΑWuR4 → ΦZNΔs8 → ΝgIΙlG → wq4ΨbW → ΤQEΝΒA → ΙyaqTK → oVFΜwe → wR9ΣΑW → ΙZPΒsK → ocIΙpe → qD9ΣΟc → ΙΒDΞQK → ΑoaqdS → YGAΡΜu → ΗvLΖWM → ljOΓih → e40γΩo → γΥ9Σ82 → αΜΘJG4 → ΦvndW8 → ΝP9ΣΓG → ΙwcoVK → oRBΠΑe → ΕZ9ΣsO → ΙgIΙlK → qo4Ψdc → ΤEAΡΞA → ΙΗySLK → olVvge → QA4ΨΣΓ → ΤΘbpKA → ΙnDΞeK → Αo8ΤdS → ΛYAΡtI → ΗsKΗZM → mkIΙhg → q62αΧc → ΨΠDΞC6 → ΡΔzROC → ΕfXtmO → gM6ΦΖm → Οj5ΧiE → ΡΑ0γRC → γΕYsN2 → αhJΘk4 → Φo2αd8 → ΨΝAΡF6 → ΡΗwULC → ΕlRzgO → gY4Ψtm → ΤL5ΧΗA → ΡΙkgJC → Εp3ΩcO → ΦgCΟl8 → ΝΓ4ΨPG → ΤwcoVA → ΙRBΠΑK → ΕoYsdO → gKAΡΘm → Ηn5ΧeM → Ρk8ΤhC → ΛΕ2αNI → ΨsgkZ6 → ΡJ3ΩΙC → ΦΕocN8 → ΝhBΠkG → Εw2αVO → ΨgQΑl6 → Ρa4ΨrC → ΤΕGΛNA → ΙugkXK → oN3ΩΕe → Φh9Σk8 → ΝΙ2αJG → ΨwocV6 → ΡRBΠΑC → ΖΔYsON → ifJΘmk → o71βΦe → αΞ9ΣE4 → ΦΙySJ8 → ΝpVvcG → wQCΟΒW → ΓbPΒqQ → dbEΝqp → yFBΠΝU → ΕxTxUO → gUSyxm → WT5Χyw → ΡVPΒwC → ΕcQΑpO → gaCΟrm → ΓH5ΧΛQ → ΡtbpYC → ΕLDΞΗO → ΑlflgS → Y64ΨΧu → ΤΠLΖCA → ΙΔjhOK → of1βme → αA6ΦΣ4 → ΦΟΗKD8 → ΝΒlfQG → wb5ΧqW → ΡQEΝΒC → ΕyaqTO → gVFΜwm → wR5ΧΑW → ΡZPΒsC → ΕcIΙpO → qgCΟlc → ΓE4ΨΞQ → ΤzbpSA → ΙXDΞuK → ΑoMΕdS → iYAΡtk → ΗL1βΗM → αljhg4 → Φ51βΨ8 → αΣΜFA4 → ΦΘvVK8 → ΝnPΒeG → wc8ΤpW → ΛQCΟΒI → ΓsaqZQ → cJFΜΙq → wpDΞcW → ΑQCΟΒS → ΓbXtqQ → cMEΝΖq → yjDΞiU → ΑU0γxS → γYSyt2 → αWKΗv4 → ΦmOΓf8 → Νe6ΦnG → Οw8ΤVE → ΛΑQΑRI → saYsra ⮌
8,874,697×12 nodes⮎ VTEΝyx → yVRzwU → YUQΑxu → aTLΖys → kVHΚwi → sR1βΑa → αZHΚs4 → ΦsIΙZ8 → ΝqIΙbG → wqEΝbW → yQEΝΒU → ybTxqU ⮌
888,596×7 nodes⮎ ib1βqk → αF1βΝ4 → αΦwU74 → ΦΞRzE8 → ΝzXtSG → wXLΖuW → kQMΕΒi ⮌
524,836×3 nodes⮎ ΑmCΟfS → ΓY6ΦtQ → ΟcKΗpE ⮌
48,334×(fixed) 1 node ⮎ ΓcCΟpQ ⮌
2,070×(fixed) 1 node ⮎ jiδδij ⮌
71 cycle 11,919,192,390×(max) 4 nodes⮎ ΖiKδΗjN → ΘjMδΕiL → ΗlLδΖgM → ΗkOδΓhM ⮌
8+---Not showing digit sets 8+ due to verbosity.