Base 102: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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 5,151×(max) 51 nodes⮎ 0π → ο1 → ν3 → ι7 → αF → ΙV → cΒ → OΠ → qn → 2ξ → λ5 → εB → ΡN → sl → 6κ → γD → ΝR → kt → 8θ → ΨH → ΕZ → UΚ → ez → KΥ → yf → IΧ → Γb → QΞ → mr → 4μ → η9 → ΦJ → Αd → MΣ → uj → Aζ → ΤL → wh → Eβ → ΛT → gx → GΩ → ΗX → YΖ → WΘ → aΔ → SΜ → iv → Cδ → ΟP → op ⮌
31 cycle 182,002×(fixed) (max) 1 node ⮎ oπp ⮌
444 cycles151,501×(max) 8 nodes⮎ 61ξλ → νδB4 → ιΠN8 → αrlG → Ι5κW → εbΒC → ΡPΞO → snpm ⮌
146,374×(max) 8 nodes⮎ A5κη → εΥJC → ΡzdO → sLΣm → w5κi → εDβC → ΡΜRO → sjtm ⮌
145,274×(max) 8 nodes⮎ IDβΨ → ΝΔZS → kTΚu → g9ζy → ΦHΧK → Εzda → ULΣΛ → wfxi ⮌
138,196×(max) 8 nodes⮎ Q5κΟ → εnpC → Ρ1ξO → νrl4 → ι5κ8 → εΩFC → ΡΘVO → sbΒm ⮌
136,517×(max) 8 nodes⮎ cTΚΓ → gPΞy → oHΧq → Ε1ξa → νTΚ4 → ιfx8 → αHΧG → ΙΔZW ⮌
135,195×(max) 8 nodes⮎ MDβΤ → ΝvhS → kDβu → Ν9ζS → ΦjtK → Α9ζe → ΦLΣK → Αvhe ⮌
134,909×(max) 8 nodes⮎ cLΣΓ → wPΞi → oDβq → Ν1ξS → νjt4 → ι9ζ8 → αΥJG → ΙzdW ⮌
134,811×(max) 8 nodes⮎ cPΞΓ → oPΞq → o1ξq → ν1ξ4 → νθ74 → ιΩF8 → αΘVG → ΙbΒW ⮌
134,733×(max) 8 nodes⮎ Y1ξΗ → νXΖ4 → ιXΖ8 → αXΖG → ΙXΖW → cXΖΓ → YPΞΗ → oXΖq ⮌
133,331×(max) 8 nodes⮎ Q9ζΟ → ΦnpK → Α1ξe → νLΣ4 → ιvh8 → αDβG → ΝΘVS → kbΒu ⮌
133,115×(max) 8 nodes⮎ I9ζΨ → ΦΔZK → ΑTΚe → gLΣy → wHΧi → ΕDβa → ΝTΚS → kfxu ⮌
132,739×(max) 8 nodes⮎ c5κΓ → εPΞC → ΡnpO → s1ξm → ν5κ4 → ιδB8 → αΠNG → ΙrlW ⮌
132,515×(max) 8 nodes⮎ I1ξΨ → νΔZ4 → ιTΚ8 → αfxG → ΙHΧW → ΕbΒa → UPΞΛ → ofxq ⮌
132,197×(max) 8 nodes⮎ MHΧΤ → Εvha → UDβΛ → ΝfxS → kHΧu → Ε9ζa → ΦTΚK → Αfxe ⮌
131,971×(max) 8 nodes⮎ QHΧΟ → Εnpa → U1ξΛ → νfx4 → ιHΧ8 → αΔZG → ΙTΚW → gbΒy ⮌
131,847×(max) 8 nodes⮎ E5κγ → εΜRC → ΡjtO → s9ζm → Φ5κK → εzdC → ΡLΣO → wrli ⮌
131,139×(max) 8 nodes⮎ M5κΤ → εvhC → ΡDβO → ΝrlS → k5κu → ε9ζC → ΦΠNK → Αrle ⮌
128,963×(max) 8 nodes⮎ A1ξη → νΥJ4 → ιzd8 → αLΣG → ΙvhW → cDβΓ → ΝPΞS → ojtq ⮌
128,759×(max) 8 nodes⮎ E1ξγ → νΜR4 → ιjt8 → α9ζG → ΦΘVK → ΑbΒe → QLΣΟ → wnpi ⮌
128,739×(max) 8 nodes⮎ E9ζγ → ΦΜRK → Αjte → M9ζΤ → ΦvhK → ΑDβe → ΝLΣS → wjti ⮌
121,248×(max) 8 nodes⮎ sDβm → Ν5κS → εjtC → Ρ9ζO → ΦrlK → Α5κe → εLΣC → ΡvhO ⮌
119,960×(max) 8 nodes⮎ k9ζu → Φ9ζK → ΦzdK → ΑLΣe → wLΣi → wDβi → ΝDβS → ΝjtS ⮌
119,896×(max) 8 nodes⮎ kPΞu → o9ζq → Φ1ξK → νzd4 → ιLΣ8 → αvhG → ΙDβW → ΝbΒS ⮌
119,896×(max) 8 nodes⮎ oLΣq → w1ξi → νDβ4 → ιΜR8 → αjtG → Ι9ζW → ΦbΒK → ΑPΞe ⮌
119,832×(max) 8 nodes⮎ c1ξΓ → νPΞ4 → ιnp8 → α1ξG → νΘV4 → ιbΒ8 → αPΞG → ΙnpW ⮌
118,112×(max) 8 nodes⮎ U9ζΛ → ΦfxK → ΑHΧe → ΕLΣa → wTΚi → gDβy → ΝHΧS → Εjta ⮌
118,048×(max) 8 nodes⮎ cHΧΓ → ΕPΞa → oTΚq → g1ξy → νHΧ4 → ιΔZ8 → αTΚG → ΙfxW ⮌
117,952×(max) 8 nodes⮎ o5κq → ε1ξC → νΠN4 → ιrl8 → α5κG → εΘVC → ΡbΒO → sPΞm ⮌
115,176×(max) 8 nodes⮎ Y9ζΗ → ΦXΖK → ΑXΖe → YLΣΗ → wXΖi → YDβΗ → ΝXΖS → kXΖu ⮌
115,048×(max) 8 nodes⮎ M1ξΤ → νvh4 → ιDβ8 → αΜRG → ΙjtW → c9ζΓ → ΦPΞK → Αnpe ⮌
115,048×(max) 8 nodes⮎ QDβΟ → ΝnpS → k1ξu → ν9ζ4 → ιΥJ8 → αzdG → ΙLΣW → wbΒi ⮌
114,984×(max) 8 nodes⮎ Q1ξΟ → νnp4 → ι1ξ8 → νΩF4 → ιΘV8 → αbΒG → ΙPΞW → obΒq ⮌
72,943×4 nodes⮎ YHΧΗ → ΕXΖa → YTΚΗ → gXΖy ⮌
61,532×4 nodes⮎ Ι1ξW → νbΒ4 → ιPΞ8 → αnpG ⮌
60,912×4 nodes⮎ sHΧm → Ε5κa → εTΚC → ΡfxO ⮌
59,172×4 nodes⮎ kLΣu → w9ζi → ΦDβK → ΝzdS ⮌
59,040×4 nodes⮎ Y5κΗ → εXΖC → ΡXΖO → sXΖm ⮌
58,536×4 nodes⮎ gHΧy → ΕHΧa → ΕTΚa → gTΚy ⮌
58,488×4 nodes⮎ U5κΛ → εfxC → ΡHΧO → Εrla ⮌
58,488×4 nodes⮎ g5κy → εHΧC → ΡΔZO → sTΚm ⮌
58,440×4 nodes⮎ s5κm → ε5κC → εΠNC → ΡrlO ⮌
56,064×4 nodes⮎ I5κΨ → εΔZC → ΡTΚO → sfxm ⮌
30,432×2 nodes⮎ Ρ5κO → εrlC ⮌
28,056×2 nodes⮎ UHΧΛ → Εfxa ⮌
52 cycles101,330,270×(fixed) 1 node ⮎ ΗXπΖY ⮌
10,504×(max) 2 nodes⮎ pnπpp → pπππo ⮌
64 cycles1,805,669,351×(max) 46 nodes⮎ UO8ηΠΛ → ΨrfxmI → ΕI4λΧa → ηΔTΚaA → ΦgSΛxK → ΑiGΨve → ΗMCγΣY → ΟvXΖiQ → oYCγΖq → ΟX1ξΗQ → νoYΕp4 → ιW0οΘ8 → οαaΓF2 → νΚRΜU4 → ιkeyt8 → αK8ηΥG → ΨΙyeVI → ΕdJΥΑa → ΑUMΡΚe → ufLΣyk → wJ9ζΦi → ΦΒDβcK → ΝΑOΟdS → qkMΡto → u91ξηk → νΧ9ζI4 → ιΦΓaJ8 → αΒRΜcG → ΙkOΟtW → qc8ηΒo → ΨP1ξΟI → νΕooZ4 → ιUππΙ8 → θΚNΠU9 → ΨseylI → ΕK6ιΥa → γzTΚeE → ΝgKΤxS → ykGΨtg → ΗI8ηΧY → ΨΔXΖaI → ΕYSΛΖa → iXTΚΗw → gZDβΕy → ΝVHΧΙS → ΕkcΑta ⮌
891,939×3 nodes⮎ YEAεβΗ → ΤΜXΖSM → wjXΖui ⮌
681,578×9 nodes⮎ ys0οlg → οI6ιΧ2 → νγΓaD4 → ιΞRΜQ8 → αnjtqG → ΙA2νζW → λΥbΒK6 → εzPΞeC → ΡoKΤpO ⮌
2,652×(fixed) 1 node ⮎ poππop ⮌
7+---Not showing digit sets 7+ due to verbosity.