Base 97: 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---
22 cycles4,032×(max) 21 nodes1κ → θ3 → δ7 → ΥF → ΔV → XΒ → TΖ → bx → LΞ → rh → 9β → ΠJ → vd → HΣ → zZ → PΚ → jp → 5ζ → ΩB → ΜN → nl
576×3 nodesDΧ → ΘR → ft
31 cycle 156,752×(max) 2 nodeslλn → mλm
448 cycles85,824×(max) 24 nodesbMΜy → pMΜk → p4ζk → β4ζA → βΟJA → ΠudK → vGΣe → ΒGΣY → ΒSΖY → dSΖw → dIΠw → xIΠc → xKΞc → tKΞg → tCΧg → ΚCΧQ → ΚipQ → j6δq → Χ6δE → ΧΗRE → ΘetS → fEΥu → ΖEΥU → ΖaxU
85,824×(max) 24 nodesF4ζΦ → βΕTA → ΠaxK → vMΜe → pGΣk → Β4ζY → βSΖA → ΠcvK → vIΠe → xGΣc → ΒKΞY → tSΖg → dCΧw → ΚIΠQ → xipc → L6δΟ → ΧsfE → ΘCΧS → ΚetQ → jEΥq → Ζ6δU → ΧaxE → ΘMΜS → petk
85,688×(max) 24 nodesT8βΗ → ΣcvI → zIΠa → xOΚc → lKΞo → t2θg → ζCΧ6 → ΩΙPC → ΜipO → n6δm → Χ0κE → κΗR2 → θet4 → δEΥ8 → ΥΕTG → ΔaxW → XMΜΓ → pUΔk → Z4ζΑ → βQΘA → ΠgrK → vAΩe → ΞGΣM → ΒqhY
85,688×(max) 24 nodesPEΥΛ → ΖknU → b2θy → ζMΜ6 → ΩojC → Μ4ζO → βmlA → Π0κK → κud2 → θGΣ4 → δΑX8 → ΥSΖG → ΔcvW → XIΠΓ → xUΔc → ZKΞΑ → tQΘg → hCΧs → ΚAΩQ → ΞipM → r6δi → Χ8βE → ΣΗRI → zeta
85,688×(max) 24 nodesR6δΙ → ΧgrE → ΘAΩS → ΞetM → rEΥi → Ζ8βU → ΣaxI → zMΜa → pOΚk → l4ζo → β2θA → ζΟJ6 → ΩudC → ΜGΣO → ΒmlY → T0κΗ → κcv2 → θIΠ4 → δwb8 → ΥKΞG → ΔsfW → XCΧΓ → ΚUΔQ → jYzq
85,688×(max) 24 nodesH2θΤ → ζΑX6 → ΩSΖC → ΜcvO → nIΠm → x0κc → κKΞ2 → θsf4 → δCΧ8 → ΥΙPG → ΔipW → X6δΓ → ΧUΔE → ΘYzS → fQΘu → hEΥs → ΖAΩU → ΞaxM → rMΜi → p8βk → Σ4ζI → βyZA → ΠOΚK → vkne
85,688×(max) 24 nodesP4ζΛ → βknA → Π2θK → ζud6 → ΩGΣC → ΜΑXO → nSΖm → d0κw → κIΠ2 → θwb4 → δKΞ8 → ΥsfG → ΔCΧW → ΚWΒQ → jUΔq → Z6δΑ → ΧQΘE → ΘgrS → fAΩu → ΞEΥM → ΖqhU → b8βy → ΣMΜI → zoja
85,688×(max) 24 nodesN2θΝ → ζoj6 → Ω4ζC → βΛNA → ΠmlK → v0κe → κGΣ2 → θΑX4 → δSΖ8 → ΥcvG → ΔIΠW → xWΒc → VKΞΕ → tYzg → RCΧΙ → ΚgrQ → jAΩq → Ξ6δM → ΧqhE → Θ8βS → ΣetI → zEΥa → ΖOΚU → laxo
85,688×(max) 24 nodesJ8βΡ → ΣwbI → zKΞa → tOΚg → lCΧo → Κ2θQ → ζip6 → Ω6δC → ΧΛNE → ΘmlS → f0κu → κEΥ2 → θΕT4 → δax8 → ΥMΜG → ΔojW → X4ζΓ → βUΔA → ΠYzK → vQΘe → hGΣs → ΒAΩY → ΞSΖM → rcvi
85,552×(max) 24 nodesVAΩΕ → ΞYzM → rQΘi → h8βs → ΣAΩI → ΞyZM → rOΚi → l8βo → Σ2θI → ζyZ6 → ΩOΚC → ΜknO → n2θm → ζ0κ6 → κΨB2 → θΛN4 → δml8 → Υ0κG → κΓV2 → θWΒ4 → δUΔ8 → ΥYzG → ΔQΘW → hWΒs
85,552×(max) 24 nodesR0κΙ → κgr2 → θAΩ4 → δΝL8 → ΥqhG → Δ8βW → ΣWΒI → zUΔa → ZOΚΑ → lQΘo → h2θs → ζAΩ6 → ΩΝLC → ΜqhO → n8βm → Σ0κI → κyZ2 → θOΚ4 → δkn8 → Υ2θG → ζΓV6 → ΩWΒC → ΜUΔO → nYzm
84,773×(max) 24 nodesLCΧΟ → ΚsfQ → jCΧq → Κ6δQ → ΧipE → Θ6δS → ΧetE → ΘEΥS → ΖetU → bEΥy → ΖMΜU → paxk → N4ζΝ → βojA → Π4ζK → βudA → ΠGΣK → ΒudY → TGΣΗ → ΒcvY → TIΠΗ → xcvc → LIΠΟ → xsfc
84,683×(max) 24 nodesFCΧΦ → ΚΕTQ → jaxq → N6δΝ → ΧojE → Θ4ζS → βetA → ΠEΥK → ΖudU → bGΣy → ΒMΜY → pSΖk → d4ζw → βIΠA → ΠwbK → vKΞe → tGΣg → ΒCΧY → ΚSΖQ → jcvq → J6δΡ → ΧwbE → ΘKΞS → tetg
84,645×(max) 24 nodesJAΩΡ → ΞwbM → rKΞi → t8βg → ΣCΧI → ΚyZQ → jOΚq → l6δo → Χ2θE → ζΗR6 → ΩetC → ΜEΥO → ΖmlU → b0κy → κMΜ2 → θoj4 → δ4ζ8 → βΤFA → ΠΓVK → vWΒe → VGΣΕ → ΒYzY → TQΘΗ → hcvs
84,627×(max) 24 nodesLAΩΟ → ΞsfM → rCΧi → Κ8βQ → ΣipI → z6δa → ΧOΚE → ΘknS → f2θu → ζEΥ6 → ΩΕTC → ΜaxO → nMΜm → p0κk → κ4ζ2 → θα94 → δΟJ8 → ΥudG → ΔGΣW → ΒWΒY → VSΖΕ → dYzw → RIΠΙ → xgrc
84,611×(max) 24 nodesL4ζΟ → βsfA → ΠCΧK → ΚudQ → jGΣq → Β6δY → ΧSΖE → ΘcvS → fIΠu → xEΥc → ΖKΞU → taxg → NCΧΝ → ΚojQ → j4ζq → β6δA → ΧΟJE → ΘudS → fGΣu → ΒEΥY → ΖSΖU → daxw → NIΠΝ → xojc
84,553×(max) 24 nodesH6δΤ → ΧΑXE → ΘSΖS → fcvu → JEΥΡ → ΖwbU → bKΞy → tMΜg → pCΧk → Κ4ζQ → βipA → Π6δK → ΧudE → ΘGΣS → ΒetY → TEΥΗ → ΖcvU → bIΠy → xMΜc → pKΞk → t4ζg → βCΧA → ΠΙPK → vipe
84,519×(max) 24 nodesB2θα → ζΝL6 → ΩqhC → Μ8βO → ΣmlI → z0κa → κOΚ2 → θkn4 → δ2θ8 → ζΤF6 → ΩΓVC → ΜWΒO → nUΔm → Z0κΑ → κQΘ2 → θgr4 → δAΩ8 → ΥΝLG → ΔqhW → X8βΓ → ΣUΔI → zYza → ROΚΙ → lgro
84,431×(max) 24 nodesP2θΛ → ζkn6 → Ω2θC → ζΛN6 → ΩmlC → Μ0κO → κml2 → θ0κ4 → κγ72 → θΤF4 → δΓV8 → ΥWΒG → ΔUΔW → ZWΒΑ → VQΘΕ → hYzs → RAΩΙ → ΞgrM → rAΩi → Ξ8βM → ΣqhI → z8βa → ΣOΚI → zkna
84,351×(max) 24 nodesFAΩΦ → ΞΕTM → raxi → N8βΝ → ΣojI → z4ζa → βOΚA → ΠknK → v2θe → ζGΣ6 → ΩΑXC → ΜSΖO → ncvm → J0κΡ → κwb2 → θKΞ4 → δsf8 → ΥCΧG → ΚΓVQ → jWΒq → V6δΕ → ΧYzE → ΘQΘS → hets
84,311×(max) 24 nodesB8βα → ΣΝLI → zqha → P8βΛ → ΣknI → z2θa → ζOΚ6 → ΩknC → Μ2θO → ζml6 → Ω0κC → κΛN2 → θml4 → δ0κ8 → κΤF2 → θΓV4 → δWΒ8 → ΥUΔG → ΔYzW → XQΘΓ → hUΔs → ZAΩΑ → ΞQΘM → rgri
84,195×(max) 24 nodes72θε → ζΦD6 → ΩΗRC → ΜetO → nEΥm → Ζ0κU → κax2 → θMΜ4 → δoj8 → Υ4ζG → βΓVA → ΠWΒK → vUΔe → ZGΣΑ → ΒQΘY → hSΖs → dAΩw → ΞIΠM → xqhc → L8βΟ → ΣsfI → zCΧa → ΚOΚQ → lipo
83,901×(max) 24 nodes94ζγ → βΡHA → ΠyZK → vOΚe → lGΣo → Β2θY → ζSΖ6 → ΩcvC → ΜIΠO → xmlc → L0κΟ → κsf2 → θCΧ4 → δΙP8 → ΥipG → Δ6δW → ΧWΒE → ΘUΔS → fYzu → REΥΙ → ΖgrU → bAΩy → ΞMΜM → roji
83,801×(max) 24 nodesHCΧΤ → ΚΑXQ → jSΖq → d6δw → ΧIΠE → ΘwbS → fKΞu → tEΥg → ΖCΧU → ΚaxQ → jMΜq → p6δk → Χ4ζE → βΗRA → ΠetK → vEΥe → ΖGΣU → ΒaxY → TMΜΗ → pcvk → J4ζΡ → βwbA → ΠKΞK → vsfe
83,671×(max) 24 nodesLGΣΟ → ΒsfY → TCΧΗ → ΚcvQ → jIΠq → x6δc → ΧKΞE → ΘsfS → fCΧu → ΚEΥQ → ΖipU → b6δy → ΧMΜE → ΘojS → f4ζu → βEΥA → ΠΕTK → vaxe → NGΣΝ → ΒojY → T4ζΗ → βcvA → ΠIΠK → xudc
83,397×(max) 24 nodesD2θΨ → ζΙP6 → ΩipC → Μ6δO → ΧmlE → Θ0κS → κet2 → θEΥ4 → δΕT8 → ΥaxG → ΔMΜW → pWΒk → V4ζΕ → βYzA → ΠQΘK → vgre → HAΩΤ → ΞΑXM → rSΖi → d8βw → ΣIΠI → zwba → PKΞΛ → tkng
83,348×(max) 24 nodes74ζε → βΦDA → ΠΗRK → vete → HEΥΤ → ΖΑXU → bSΖy → dMΜw → pIΠk → x4ζc → βKΞA → ΠsfK → vCΧe → ΚGΣQ → ΒipY → T6δΗ → ΧcvE → ΘIΠS → xetc → LEΥΟ → ΖsfU → bCΧy → ΚMΜQ → pipk
83,206×(max) 24 nodes52θη → ζα96 → ΩΟJC → ΜudO → nGΣm → Β0κY → κSΖ2 → θcv4 → δIΠ8 → ΥwbG → ΔKΞW → tWΒg → VCΧΕ → ΚYzQ → jQΘq → h6δs → ΧAΩE → ΞΗRM → reti → F8βΦ → ΣΕTI → zaxa → PMΜΛ → pknk
83,198×(max) 24 nodes96δγ → ΧΡHE → ΘyZS → fOΚu → lEΥo → Ζ2θU → ζax6 → ΩMΜC → ΜojO → n4ζm → β0κA → κΟJ2 → θud4 → δGΣ8 → ΥΑXG → ΔSΖW → dWΒw → VIΠΕ → xYzc → RKΞΙ → tgrg → DAΩΨ → ΞΙPM → ripi
82,901×(max) 24 nodesD6δΨ → ΧΙPE → ΘipS → f6δu → ΧEΥE → ΘΕTS → faxu → NEΥΝ → ΖojU → b4ζy → βMΜA → ΠojK → v4ζe → βGΣA → ΠΑXK → vSΖe → dGΣw → ΒIΠY → xSΖc → dKΞw → tIΠg → xCΧc → ΚKΞQ → tipg
82,432×(max) 24 nodes30κι → κε52 → θΨB4 → δΛN8 → ΥmlG → Δ0κW → κWΒ2 → θUΔ4 → δYz8 → ΥQΘG → ΔgrW → XAΩΓ → ΞUΔM → rYzi → R8βΙ → ΣgrI → zAΩa → ΞOΚM → rkni → 92θγ → ζΡH6 → ΩyZC → ΜOΚO → nknm
82,088×(max) 24 nodesB4ζα → βΝLA → ΠqhK → v8βe → ΣGΣI → ΒyZY → TOΚΗ → lcvo → J2θΡ → ζwb6 → ΩKΞC → ΜsfO → nCΧm → Κ0κQ → κip2 → θ6δ4 → δΦD8 → ΥΗRG → ΔetW → XEΥΓ → ΖUΔU → bYzy → RMΜΙ → pgrk
82,071×(max) 24 nodes90κγ → κΡH2 → θyZ4 → δOΚ8 → ΥknG → Δ2θW → ζWΒ6 → ΩUΔC → ΜYzO → nQΘm → h0κs → κAΩ2 → θΝL4 → δqh8 → Υ8βG → ΣΓVI → zWΒa → VOΚΕ → lYzo → R2θΙ → ζgr6 → ΩAΩC → ΞΛNM → rmli
82,005×(max) 24 nodesH8βΤ → ΣΑXI → zSΖa → dOΚw → lIΠo → x2θc → ζKΞ6 → ΩsfC → ΜCΧO → ΚmlQ → j0κq → κ6δ2 → θΦD4 → δΗR8 → ΥetG → ΔEΥW → ΖWΒU → bUΔy → ZMΜΑ → pQΘk → h4ζs → βAΩA → ΠΝLK → vqhe
81,795×(max) 24 nodesNAΩΝ → ΞojM → r4ζi → β8βA → ΣΟJI → zuda → PGΣΛ → ΒknY → T2θΗ → ζcv6 → ΩIΠC → ΜwbO → nKΞm → t0κg → κCΧ2 → θΙP4 → δip8 → Υ6δG → ΧΓVE → ΘWΒS → fUΔu → ZEΥΑ → ΖQΘU → haxs
81,650×(max) 24 nodesF6δΦ → ΧΕTE → ΘaxS → fMΜu → pEΥk → Ζ4ζU → βaxA → ΠMΜK → voje → H4ζΤ → βΑXA → ΠSΖK → vcve → JGΣΡ → ΒwbY → TKΞΗ → tcvg → JCΧΡ → ΚwbQ → jKΞq → t6δg → ΧCΧE → ΚΗRQ → jetq
81,441×(max) 24 nodesB0κα → κΝL2 → θqh4 → δ8β8 → ΥΡHG → ΔyZW → XOΚΓ → lUΔo → Z2θΑ → ζQΘ6 → ΩgrC → ΜAΩO → ΞmlM → r0κi → κ8β2 → θΡH4 → δyZ8 → ΥOΚG → ΔknW → X2θΓ → ζUΔ6 → ΩYzC → ΜQΘO → ngrm
81,416×(max) 24 nodes50κη → κα92 → θΟJ4 → δud8 → ΥGΣG → ΔΑXW → XSΖΓ → dUΔw → ZIΠΑ → xQΘc → hKΞs → tAΩg → ΞCΧM → ΚqhQ → j8βq → Σ6δI → ΧyZE → ΘOΚS → leto → F2θΦ → ζΕT6 → ΩaxC → ΜMΜO → pmlk
81,389×(max) 24 nodesXUΔΓ → ZUΔΑ → ZQΘΑ → hQΘs → hAΩs → ΞAΩM → ΞqhM → r8βi → Σ8βI → ΣyZI → zOΚa → lOΚo → l2θo → ζ2θ6 → ζΨB6 → ΩΛNC → ΜmlO → n0κm → κ0κ2 → κη32 → θγ74 → δΤF8 → ΥΓVG → ΔWΒW
81,351×(max) 24 nodesD0κΨ → κΙP2 → θip4 → δ6δ8 → ΧΤFE → ΘΓVS → fWΒu → VEΥΕ → ΖYzU → bQΘy → hMΜs → pAΩk → Ξ4ζM → βqhA → Π8βK → ΣudI → zGΣa → ΒOΚY → lSΖo → d2θw → ζIΠ6 → ΩwbC → ΜKΞO → tmlg
81,117×(max) 24 nodesF0κΦ → κΕT2 → θax4 → δMΜ8 → ΥojG → Δ4ζW → βWΒA → ΠUΔK → vYze → RGΣΙ → ΒgrY → TAΩΗ → ΞcvM → rIΠi → x8βc → ΣKΞI → zsfa → PCΧΛ → ΚknQ → j2θq → ζ6δ6 → ΩΦDC → ΜΗRO → netm
80,231×(max) 24 nodesP0κΛ → κkn2 → θ2θ4 → ζγ76 → ΩΤFC → ΜΓVO → nWΒm → V0κΕ → κYz2 → θQΘ4 → δgr8 → ΥAΩG → ΞΓVM → rWΒi → V8βΕ → ΣYzI → zQΘa → hOΚs → lAΩo → Ξ2θM → ζqh6 → Ω8βC → ΣΛNI → zmla
79,965×(max) 24 nodesPAΩΛ → ΞknM → r2θi → ζ8β6 → ΩΡHC → ΜyZO → nOΚm → l0κo → κ2θ2 → θε54 → δΨB8 → ΥΛNG → ΔmlW → X0κΓ → κUΔ2 → θYz4 → δQΘ8 → ΥgrG → ΔAΩW → ΞWΒM → rUΔi → Z8βΑ → ΣQΘI → zgra
79,648×(max) 24 nodes70κε → κΦD2 → θΗR4 → δet8 → ΥEΥG → ΖΓVU → bWΒy → VMΜΕ → pYzk → R4ζΙ → βgrA → ΠAΩK → ΞudM → rGΣi → Β8βY → ΣSΖI → zcva → PIΠΛ → xknc → L2θΟ → ζsf6 → ΩCΧC → ΜΙPO → nipm
79,464×(max) 24 nodesB6δα → ΧΝLE → ΘqhS → f8βu → ΣEΥI → ΖyZU → bOΚy → lMΜo → p2θk → ζ4ζ6 → βΨBA → ΠΛNK → vmle → H0κΤ → κΑX2 → θSΖ4 → δcv8 → ΥIΠG → ΔwbW → XKΞΓ → tUΔg → ZCΧΑ → ΚQΘQ → jgrq
78,724×(max) 24 nodesD8βΨ → ΣΙPI → zipa → P6δΛ → ΧknE → Θ2θS → ζet6 → ΩEΥC → ΜΕTO → naxm → N0κΝ → κoj2 → θ4ζ4 → δα98 → ΥΟJG → ΔudW → XGΣΓ → ΒUΔY → ZSΖΑ → dQΘw → hIΠs → xAΩc → ΞKΞM → tqhg
42,776×12 nodesV2θΕ → ζYz6 → ΩQΘC → ΜgrO → nAΩm → Ξ0κM → κqh2 → θ8β4 → δΡH8 → ΥyZG → ΔOΚW → lWΒo
41,875×12 nodesD4ζΨ → βΙPA → ΠipK → v6δe → ΧGΣE → ΘΑXS → fSΖu → dEΥw → ΖIΠU → xaxc → NKΞΝ → tojg
52 cycles52,703,413×3 nodesΓUλΔX → ΕVλΓV → ΔYλzW
26,505,235×(max) 4 nodesΓVλΓX → ΔUλΔW → ΕWλΒV → ΔXλΑW
67 cycles565,909,854×13 nodesVH3ηΣΕ → δΑYzY8 → ΥSQΘΗG → ΔhdurW → XH9αΣΓ → ΠΑUΔYK → vZRΗze → fQGΣΙu → ΒiEΥqY → ΖT7γΖU → ΥcaxwG → ΔNJΟΜW → voWΒke
529,395,359×(max) 18 nodesPD1ιΧΛ → θΙknQ4 → δi2θq8 → ζΥ7γF6 → ΩΥΔUFC → ΜΕYzUO → naQΘym → hO0κΛs → κmAΩm2 → θΝλλL4 → ηΞIΠL5 → βxrgbA → ΠMAΩΝK → ΞvpidM → rI6δΡi → Χy8βaE → ΣΘNΛRI → znfsla
222,347,769×10 nodesNH3ηΣΝ → δΑojY8 → ΥS4ζΗG → βΔduVA → ΠYGΣΑK → ΒvRΗdY → fTHΡΖu → zcEΥwa → ΖPJΟΚU → vkaxoe
20,370,832×13 nodestSλλΖg → ΗsBΨgT → ΜdBΨvO → ΜnHΡlO → zn1ιla → θP1ιΚ4 → θδjo74 → δΦ4ζE8 → βΥΖSFA → ΠΕcvUK → vaIΠye → xOGΣΛc → ΒmKΞmY
6,208,842×3 nodesvTDΦΖe → ΘcGΣwS → ΒfJΟtY
1,654,855×(fixed) 1 node ΘfDΦtS
661,057×3 nodesδa0κy8 → κΥNΛF2 → θΕmlU4
73 cycles16,230,730,643×2 nodesΛnNλΛlP → ΜlOλΚnO
1,820,289,860×2 nodesΜnMλΜlO → ΝnPλΙlN
1,762,481,185×(max) 4 nodesΚlMλΜnQ → ΝlNλΛnN → ΜpOλΚjO → ΛnPλΙlP
8+---Not showing digit sets 8+ due to verbosity.