Base 106: 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 5,565×(max) 53 nodes0τ → σ1 → ρ3 → ν7 → εF → ΝV → gΒ → KΩ → Γf → MΧ → yj → Eζ → ΟT → kx → Cθ → ΤP → sp → 2ς → ο5 → ιB → ΦN → wl → Aκ → ΨL → Αh → Iβ → Ηb → UΞ → iz → Gδ → ΛX → cΖ → SΠ → mv → 8μ → γH → ΙZ → YΚ → aΘ → WΜ → eΔ → OΥ → un → 6ξ → ηD → ΡR → ot → 4π → λ9 → αJ → Εd → QΣ → qr
31 cycle 204,050×(fixed) (max) 1 node qτr
413 cycles448,177×(max) 26 nodesM5ξΨ → ιzhC → ΦHβO → Ιvla → Y9κΛ → αbΖK → ΕTΞe → kPΣy → sDζq → Ρ1ςS → ρnt4 → ν5ξ8 → ιδFC → ΦΜVO → wfΒm → M9κΨ → αzhK → ΕHβe → ΙPΣa → sXΚq → c1ςΗ → ρTΞ4 → νjx8 → εDζG → ΡΜVS → ofΒu
448,022×(max) 26 nodesIDζγ → ΡΘZS → oXΚu → c5ξΗ → ιTΞC → ΦjxO → wDζm → Ρ9κS → αntK → Ε5ξe → ιPΣC → ΦrpO → w1ςm → ρ9κ4 → νΩJ8 → εΔdG → ΝPΣW → sfΒq → M1ςΨ → ρzh4 → νHβ8 → εΘZG → ΝXΚW → gbΖΓ → ULΧΟ → Αjxi
448,018×(max) 26 nodesA1ςλ → ρΩJ4 → νΔd8 → εPΣG → ΝrpW → g1ςΓ → ρLΧ4 → νzh8 → εHβG → ΝΘZW → gXΚΓ → cLΧΗ → ΑTΞi → kHβy → ΙDζa → ΡXΚS → obΖu → U5ξΟ → ιjxC → ΦDζO → ΡvlS → o9κu → α5ξK → ιΔdC → ΦPΣO → wrpm
447,386×(max) 26 nodescTΞΗ → kTΞy → kDζy → ΡDζS → ΡntS → o5ξu → ι5ξC → ιΥNC → ΦvlO → w9κm → α9κK → αΔdK → ΕPΣe → sPΣq → s1ςq → ρ1ς4 → ρμ74 → νδF8 → εΜVG → ΝfΒW → gLΧΓ → ΑLΧi → ΑHβi → ΙHβa → ΙXΚa → cXΚΗ
446,990×(max) 26 nodesA5ξλ → ιΩJC → ΦΔdO → wPΣm → s9κq → α1ςK → ρΔd4 → νPΣ8 → εrpG → Ν1ςW → ρfΒ4 → νLΧ8 → εzhG → ΝHβW → ΙfΒa → YLΧΛ → ΑbΖi → UHβΟ → Ιjxa → YDζΛ → ΡbΖS → oTΞu → k5ξy → ιDζC → ΦΠRO → wntm
446,758×(max) 26 nodesQDζΤ → ΡrpS → o1ςu → ρ5ξ4 → νθB8 → εΥNG → ΝvlW → g9κΓ → αLΧK → Εzhe → QHβΤ → Ιrpa → Y1ςΛ → ρbΖ4 → νTΞ8 → εjxG → ΝDζW → ΡfΒS → oLΧu → Α5ξi → ιHβC → ΦΘZO → wXΚm → c9κΗ → αTΞK → Εjxe
445,071×(max) 26 nodes61ςο → ρθB4 → νΥN8 → εvlG → Ν9κW → αfΒK → ΕLΧe → ΑPΣi → sHβq → Ι1ςa → ρXΚ4 → νbΖ8 → εTΞG → ΝjxW → gDζΓ → ΡLΧS → Αnti → I5ξγ → ιΘZC → ΦXΚO → wbΖm → U9κΟ → αjxK → ΕDζe → ΡPΣS → sntq
444,312×(max) 26 nodesE5ξη → ιΠRC → ΦntO → w5ξm → ι9κC → αΥNK → Εvle → Q9κΤ → αrpK → Ε1ςe → ρPΣ4 → νrp8 → ε1ςG → ρΜV4 → νfΒ8 → εLΧG → ΝzhW → gHβΓ → ΙLΧa → ΑXΚi → cHβΗ → ΙTΞa → kXΚy → cDζΗ → ΡTΞS → ojxu
443,930×(max) 26 nodesI1ςγ → ρΘZ4 → νXΚ8 → εbΖG → ΝTΞW → kfΒy → MDζΨ → ΡzhS → oHβu → Ι5ξa → ιXΚC → ΦbΖO → wTΞm → k9κy → αDζK → ΡΔdS → oPΣu → s5ξq → ι1ςC → ρΥN4 → νvl8 → ε9κG → αΜVK → ΕfΒe → QLΧΤ → Αrpi
443,100×(max) 26 nodesMHβΨ → Ιzha → YHβΛ → ΙbΖa → YTΞΛ → kbΖy → UDζΟ → ΡjxS → oDζu → Ρ5ξS → ιntC → Φ5ξO → ιvlC → Φ9κO → αvlK → Ε9κe → αPΣK → Εrpe → Q1ςΤ → ρrp4 → ν1ς8 → ρδF4 → νΜV8 → εfΒG → ΝLΧW → ΑfΒi
441,610×(max) 26 nodesE9κη → αΠRK → Εnte → Q5ξΤ → ιrpC → Φ1ςO → ρvl4 → ν9κ8 → εΩJG → ΝΔdW → gPΣΓ → sLΧq → Α1ςi → ρHβ4 → νΘZ8 → εXΚG → ΝbΖW → gTΞΓ → kLΧy → ΑDζi → ΡHβS → Ιnta → Y5ξΛ → ιbΖC → ΦTΞO → wjxm
439,568×(max) 26 nodesE1ςη → ρΠR4 → νnt8 → ε5ξG → ιΜVC → ΦfΒO → wLΧm → Α9κi → αHβK → ΙΔda → YPΣΛ → sbΖq → U1ςΟ → ρjx4 → νDζ8 → εΠRG → ΝntW → g5ξΓ → ιLΧC → ΦzhO → wHβm → Ι9κa → αXΚK → ΕbΖe → UPΣΟ → sjxq
220,203×13 nodesI9κγ → αΘZK → ΕXΚe → cPΣΗ → sTΞq → k1ςy → ρDζ4 → νΠR8 → εntG → Ν5ξW → ιfΒC → ΦLΧO → Αvli
53 cycles81,409,834×3 nodesΙXτΚa → ΛYτΙY → ΚbτΖZ
40,970,242×(max) 4 nodesΙYτΙa → ΚXτΚZ → ΛZτΘY → ΚaτΗZ
11,340×2 nodesrpτrr → rτττq
66 cycles1,090,972,496×(max) 253 nodesGA6νκε → ηΩΜVKE → ΡΔfΒeS → oPLΧΤu → Αt5ξoi → ιI4οβC → λΦΗaNA → αxVΜkK → ΕgCηΒe → ΤQKΨΣQ → Γsqqpg → M2ττρΨ → ςΧHβM3 → οΙyiZ6 → ιZFδΙC → ΦΝYΙVO → whZΘΑm → YJ9καΛ → αΖbΖcK → ΕUSΟΞe → mjPΣyw → sF9κεq → αΞ1ςUK → ρΕiyd4 → νRFδΡ8 → εΝosVG → Νh3πΑW → νgIαΒ8 → εΗKΨbG → ΝΓUΝfW → igMΦΒΑ → yLHβΨk → ΙΒDζga → ΡYKΨΚS → ΓoaΗtg → WM4οΧΝ → λzfΒiA → αMGγΧK → ΛΕyidY → cRFδΡΗ → ΝpTΞsW → kg2ρΒy → οLDζΨ6 → ιΡΑgRC → ΦpJΩsO → Εw2ρle → οQAιΣ6 → ιΨqqLC → ΦΑττgO → ΥΒJΩgP → ΕuKΨne → ΓQ6νΣg → ηrLΧqE → ΡΑ0σhS → σoIαt2 → ρΗ4οb4 → νλUΝ98 → εβhzIG → ΝΘHβaW → ΙgWΛΒa → eYKΨΚΕ → ΓbPΣΗg → sVLΧΝq → Αh1ςΑi → ρJHβα4 → νΙΕcZ8 → εZRΠΙG → ΝoYΙtW → ga4οΘΓ → λXLΧΛA → αΑcΕhK → ΕSIαΠe → ΗnPΣuc → sU6νΞq → ηj1ςyE → ρΡEεR4 → νΟosT8 → εl3πwG → νΝAιV8 → εΨgΑLG → ΝΒJΩgW → ΕgKΨΒe → ΓQKΨΣg → ΓrLΧqg → ΑM0σΧi → σzHβi2 → ρΙGγZ4 → νΛYΙX8 → εdZΘΕG → ΝYQΡΚW → qgaΗΒs → WL1ςΨΝ → ρΒfΒg4 → νMKΨΧ8 → εΓyifG → ΝNFδΦW → ΝxfΒkW → gMCηΧΓ → ΤzLΧiQ → ΑsGγpi → ΛI2ρβY → οΘbΖa6 → ιXTΞΛC → ΦkcΕxO → wSCηΠm → Τn9κuQ → αs6νpK → ηΕ2ρdE → οΡQΡR6 → ιqosrC → Φ40σπO → σμvl82 → ρδ9κG4 → ναΛWJ8 → εΖdΔcG → ΝTPΣΟW → slfΒwq → MB1ςιΨ → ρΧzhM4 → νzHβi8 → εΙGγZG → ΝΛYΙXW → gdZΘΕΓ → YRLΧΡΛ → ΑpbΖsi → UI2ρβΟ → οΘjxa6 → ιXDζΛC → ΦΡcΕRO → wpRΠsm → oA2ρκu → οΩ5ξK6 → κθΓeCB → ΨΥNΥOM → Αwumli → IB7μιγ → εΧΘZMG → ΝzXΚiW → gcGγΖΓ → ΛTLΧΟY → ΑlbΖwi → UIAιβΟ → ΨΘjxaM → ΑXDζΛi → ΡdHβΕS → ΙoQΡta → qY4οΚs → λb1ςΗA → ραUΝJ4 → νΖhzc8 → εTHβΟG → ΝΙkwZW → gZBθΙΓ → ΦZLΧΙO → ΑwYΙli → aIAιβΙ → ΨΘXΚaM → ΑcWΛΖi → eTHβΟΕ → ΙlPΣwa → sYAιΚq → Ψb1ςΗM → ρΑUΝh4 → νiIαz8 → εΗGγbG → ΝΛUΝXW → igcΕΒΑ → SLHβΨΡ → ΙΒntga → YL5ξΨΛ → ιΒbΖgC → ΦUKΨΞO → Γwiylg → MGAιδΨ → ΨΜzhWM → ΑfHβΓi → ΙNHβΦa → ΙxXΚka → cYCηΚΗ → ΤbTΞΗQ → skUΝxq → iD1ςηΑ → ρΣHβQ4 → νΙqqZ8 → εYττΙG → δΚJΩYH → ΛΕaΗdY → cWQΡΜΗ → qfTΞΓs → kN1ςΦy → ρxDζk4 → νΡCηR8 → εΤosPG → Νt3πoW → νg4οΒ8 → λεKΨFA → αΞΒfUK → ΕjLΧye → ΑQEεΣi → ΟrHβqU → Ιk0σxa → σYCηΚ2 → ρΤaΗP4 → νtVΜo8 → εg4οΒG → λΝKΨVA → αΓgΑfK → ΕNJΩΦe → ΕxPΣke → sQCηΣq → Τr1ςqQ → ρs0σp4 → σν2ρ72 → ροεE54 → νκΞTA8 → εΩjxKG → ΝΔDζeW → ΡgOΤΒS → uoKΨto → Γ64οξg → λθLΧCA → αΥzhOK → ΕvHβme → ΙQ8λΣa → γrXΚqI → Ιc0σΖa → σYSΟΚ2 → ρmaΗv4 → νW8λΜ8 → εγeΓHG → ΝΚNΥYW → wgaΗΒm → WL9κΨΝ → αΒfΒgK → ΕMKΨΧe → ΓzPΣig → sMGγΧq → Λz1ςiY → ρcGγΖ4 → νΛSΟX8 → εmcΕvG → ΝS8λΠW → γnfΒuI → ΙM6νΧa → ηzXΚiE → ΡcGγΖS → ΛoSΟtY → mc4οΖw → λT9κΟA → βΩkwKJ → ΗΔBθec → ΦUOΤΞO → wuiynm
803,187,998×152 nodes62ττρο → ςξ1ς63 → ροηC54 → νκΣPA8 → εΩrpKG → ΝΔ1ςeW → ρgOΤΒ4 → νuKΨn8 → εΓ6νfG → ηΝMΦVE → ΡygΑjS → oKEεΩu → ΟΔ5ξeU → ιkOΤxC → ΦuCηnO → Τw6νlQ → ηsAιpE → ΨΡ2ρRM → οΑosh6 → ιJ3παC → νΦΕcN8 → εxRΠkG → ΝoCηtW → Τg4οΒQ → λsKΨpA → αΓ2ρfK → οΕMΦd6 → ιyQΡjC → ΦqEεrO → Οw0σlU → σkAιx2 → ρΨCηL4 → νΤΑgP8 → εtJΩoG → ΝΕ4οdW → λgQΡΒA → αqKΨrK → ΕΓ0σfe → σQMΦΣ2 → ρyqqj4 → νEττε8 → μζ7μE9 → εγΟSHG → ΝΚlvYW → gb9κΗΓ → αVLΧΝK → ΕΑgΑhe → QKIαΩΤ → ΗΔrpec → UP1ςΤΟ → ρtjxo4 → νE4οζ8 → λεΟSFA → αΞlvUK → Εj9κye → αQEεΣK → ΟΕqqdU → kQττΡy → ΣxHβkR → ΙqCηra → ΤY0σΚQ → σsaΗp2 → ρW2ρΜ4 → ονeΓ76 → ιζNΥEC → ΦΠvlSO → wn9κum → αA6νκK → ηΩΔdKE → ΡΔPΣeS → soOΤtq → u51ςοo → ρκ5ξA4 → νιΨKB8 → εΧΒfMG → ΝzLΧiW → ΑgGγΒi → ΛLHβΨY → ΙΒbΖga → YUKΨΞΛ → ΓjbΖyg → UMEεΧΟ → ΟzjxiU → kHDζγy → ΡΚDζYS → ΡoaΗtS → oW4οΜu → λf5ξΓA → ιαMΦJC → ΦΖxjcO → wTDζΟm → Ρl9κwS → αoAιtK → ΨΕ4οdM → λΑQΡhA → αqIαrK → ΗΕ0σdc → σUQΡΞ2 → ρqiyr4 → νG0σδ8 → σεΛWF2 → ρΞdΔU4 → νjPΣy8 → εsEεpG → ΟΝ2ρVU → οkgΑx6 → ιKCηΩC → ΦΤΓePO → wtNΥom → wA4οκm → λΩ9κKA → βΩΓeKJ → ΗΔNΥec → wUOΤΞm → uj9κyo → αF5ξεK → ιΞΔdUC → ΦjPΣyO → wsEεpm → ΟA2ρκU → οΩjxK6 → ιΔDζeC → ΦΡOΤRO → wuosnm → A73πνλ → νζΩJE8 → εΠΔdSG → ΝnPΣuW → sg6νΒq → ηL1ςΨE → ρΡΑgR4 → νpJΩs8 → εΕ2ρdG → οΝQΡV6 → ιqgΑrC → ΦK0σΩO → σΔvle2 → ρP9κΤ4 → ναsoJ8 → εΖ3πcG → νΝSΟV8 → εmgΑvG → ΝK8λΩW → γΔfΒeI → ΙPLΧΤa → ΑtXΚoi → cI4οβΗ → λΘTΞaA → αkWΛxK → ΕeCηΔe → ΤQOΤΣQ → usqqpo
241,588,176×107 nodesGA2ρκε → οΩΜVK6 → ιΔfΒeC → ΦPLΧΤO → Αwsoli → IB3πιγ → νΧΘZM8 → εzXΚiG → ΝcGγΖW → ΛgSΟΒY → mcKΨΖw → ΓT9κΟg → αlLΧwK → ΕΑAιhe → ΨQIαΣM → ΗΑqqhc → UIτταΟ → βΞ9κUJ → αΗiybK → ΕVFδΝe → ΝhPΣΑW → sgIαΒq → ΗL1ςΨc → ρΒTΞg4 → νkKΨx8 → εΓCηfG → ΤΝMΦVQ → ysgΑpk → KE2ρζα → οΠΔdS6 → ιnPΣuC → Φs6νpO → ηw2ρlE → οΡAιR6 → ιΨosLC → ΦΒ3πgO → νwKΨl8 → εΓAιfG → ΨΝMΦVM → ΑygΑji → KIEεβα → ΟΘΔdaU → kXPΣΛy → sdDζΕq → ΡR1ςΡS → ρpnts4 → ν62ρξ8 → οθδFC6 → ιΥΜVOC → ΦvfΒmO → wM8λΧm → γz9κiI → αΙGγZK → ΛΕYΙdY → caQΡΘΗ → qXTΞΛs → kd1ςΕy → ρRDζΡ4 → νΡosR8 → εp3πsG → νΝ2ρV8 → οεgΑF6 → ιΞJΩUC → ΦΕiydO → wRFδΡm → Νp9κsW → αg2ρΒK → οΕKΨd6 → ιΓQΡfC → ΦqMΦrO → yw0σlk → σEAιζ2 → ρΨΟSL4 → νΒlvg8 → εL9κΨG → αΝΑgVK → ΕhJΩΑe → ΕQIαΣe → ΗrPΣqc → sU0σΞq → σj1ςy2 → ςπEε43 → ομΞT86 → ιδjxGC → ΦΜDζWO → ΡweΓlS → oOAιΥu → Ψv5ξmM → ιΑ8λhC → γΦIαNI → ΙΗwkba → YVBθΝΛ → ΦhbΖΑO → wUIαΞm → Ηj9κyc → αUEεΞK → ΟΕiydU → kRFδΡy → ΝpDζsW → Ρg2ρΒS → οoKΨt6 → ιΓ4οfC → λΦMΦNA → αywkjK → ΕFBθεe → ΦΞPΣUO → wsiypm
102,287,153×27 nodesUB7μιΟ → εΧjxMG → ΝzDζiW → ΡgGγΒS → ΛoKΨtY → Γc4οΖg → λTLΧΟA → αΑkwhK → ΕJBθαe → ΦΖPΣcO → wsSΟpm → mA2ρκw → οΩ9κK6 → ιαΓeJC → ΦΖNΥcO → xvSΟml → mC8λθw → γΥ9κOI → αΙumZK → ΕZ7μΙe → εZPΣΙG → ΝsYΙpW → ga2ρΘΓ → οXLΧΛ6 → ιΑcΕhC → ΦSIαΠO → Ηwmulc
26,204,366×5 nodesiTHβΟΑ → ΙlHβwa → ΙYAιΚa → ΨbXΚΗM → ΑcUΝΖi
2,862×(fixed) 1 node rqττqr
7+---Not showing digit sets 7+ due to verbosity.