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 nodes⮎ 1κ → θ3 → δ7 → ΥF → ΔV → XΒ → TΖ → bx → LΞ → rh → 9β → ΠJ → vd → HΣ → zZ → PΚ → jp → 5ζ → ΩB → ΜN → nl ⮌
576×3 nodes⮎ DΧ → ΘR → ft ⮌
31 cycle 156,752×(max) 2 nodes⮎ lλn → mλm ⮌
448 cycles85,824×(max) 24 nodes⮎ bMΜy → 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 nodes⮎ F4ζΦ → 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 nodes⮎ T8βΗ → 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 nodes⮎ PEΥΛ → 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 nodes⮎ R6δΙ → 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 nodes⮎ H2θΤ → 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 nodes⮎ P4ζΛ → 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 nodes⮎ N2θΝ → 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 nodes⮎ J8βΡ → 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 nodes⮎ VAΩΕ → 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 nodes⮎ R0κΙ → 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 nodes⮎ LCΧΟ → 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 nodes⮎ FCΧΦ → 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 nodes⮎ JAΩΡ → 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 nodes⮎ LAΩΟ → 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 nodes⮎ L4ζΟ → 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 nodes⮎ H6δΤ → 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 nodes⮎ B2θα → 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 nodes⮎ P2θΛ → 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 nodes⮎ FAΩΦ → 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 nodes⮎ B8βα → 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 nodes⮎ 72θε → 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 nodes⮎ 94ζγ → 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 nodes⮎ HCΧΤ → 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 nodes⮎ LGΣΟ → 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 nodes⮎ D2θΨ → 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 nodes⮎ 74ζε → 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 nodes⮎ 52θη → 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 nodes⮎ 96δγ → 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 nodes⮎ D6δΨ → 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 nodes⮎ 30κι → 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 nodes⮎ B4ζα → 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 nodes⮎ 90κγ → 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 nodes⮎ H8βΤ → 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 nodes⮎ NAΩΝ → 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 nodes⮎ F6δΦ → 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 nodes⮎ B0κα → 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 nodes⮎ 50κη → 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 nodes⮎ XUΔΓ → 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 nodes⮎ D0κΨ → 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 nodes⮎ F0κΦ → 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 nodes⮎ P0κΛ → 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 nodes⮎ PAΩΛ → 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 nodes⮎ 70κε → 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 nodes⮎ B6δα → 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 nodes⮎ D8βΨ → 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 nodes⮎ V2θΕ → ζYz6 → ΩQΘC → ΜgrO → nAΩm → Ξ0κM → κqh2 → θ8β4 → δΡH8 → ΥyZG → ΔOΚW → lWΒo ⮌
41,875×12 nodes⮎ D4ζΨ → βΙPA → ΠipK → v6δe → ΧGΣE → ΘΑXS → fSΖu → dEΥw → ΖIΠU → xaxc → NKΞΝ → tojg ⮌
52 cycles52,703,413×3 nodes⮎ ΓUλΔX → ΕVλΓV → ΔYλzW ⮌
26,505,235×(max) 4 nodes⮎ ΓVλΓX → ΔUλΔW → ΕWλΒV → ΔXλΑW ⮌
67 cycles565,909,854×13 nodes⮎ VH3ηΣΕ → δΑYzY8 → ΥSQΘΗG → ΔhdurW → XH9αΣΓ → ΠΑUΔYK → vZRΗze → fQGΣΙu → ΒiEΥqY → ΖT7γΖU → ΥcaxwG → ΔNJΟΜW → voWΒke ⮌
529,395,359×(max) 18 nodes⮎ PD1ιΧΛ → θΙknQ4 → δi2θq8 → ζΥ7γF6 → ΩΥΔUFC → ΜΕYzUO → naQΘym → hO0κΛs → κmAΩm2 → θΝλλL4 → ηΞIΠL5 → βxrgbA → ΠMAΩΝK → ΞvpidM → rI6δΡi → Χy8βaE → ΣΘNΛRI → znfsla ⮌
222,347,769×10 nodes⮎ NH3ηΣΝ → δΑojY8 → ΥS4ζΗG → βΔduVA → ΠYGΣΑK → ΒvRΗdY → fTHΡΖu → zcEΥwa → ΖPJΟΚU → vkaxoe ⮌
20,370,832×13 nodes⮎ tSλλΖg → ΗsBΨgT → ΜdBΨvO → ΜnHΡlO → zn1ιla → θP1ιΚ4 → θδjo74 → δΦ4ζE8 → βΥΖSFA → ΠΕcvUK → vaIΠye → xOGΣΛc → ΒmKΞmY ⮌
6,208,842×3 nodes⮎ vTDΦΖe → ΘcGΣwS → ΒfJΟtY ⮌
1,654,855×(fixed) 1 node ⮎ ΘfDΦtS ⮌
661,057×3 nodes⮎ δa0κy8 → κΥNΛF2 → θΕmlU4 ⮌
73 cycles16,230,730,643×2 nodes⮎ ΛnNλΛlP → ΜlOλΚnO ⮌
1,820,289,860×2 nodes⮎ ΜnMλΜlO → ΝnPλΙlN ⮌
1,762,481,185×(max) 4 nodes⮎ ΚlMλΜnQ → ΝlNλΛnN → ΜpOλΚjO → ΛnPλΙlP ⮌
8+---Not showing digit sets 8+ due to verbosity.