Base 85: 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---
23 cycles1,176×(max) 7 nodes1Χ → Υ3 → Π7 → ΘF → rV → LΒ → fh
1,176×(max) 7 nodes5Σ → ΜB → zN → bl → 9Ξ → ΔJ → jd
1,176×(max) 7 nodesDΚ → vR → Tt → Px → Xp → HΖ → nZ
31 cycle 105,910×(max) 2 nodesfΨh → gΨg
4117 cycles24,195×(max) 8 nodesN6ΠΑ → ΚcjE → v6ΠS → ΚStE → vQvS → VSts → RMzw → dUrk
24,000×(max) 8 nodesbMzm → dAΜk → Β6ΠM → ΚehE → v2ΥS → ΣSt6 → ΜQvC → zUrO
23,960×(max) 8 nodesT0Χu → ΧQv2 → ΥUr4 → ΠMz8 → ΘcjG → r6ΠW → ΚKΒE → vgfS
23,952×(max) 8 nodeshCΚg → x0ΧQ → ΧWp2 → ΥIΔ4 → Πkb8 → Θ8ΞG → ΖqVI → nKΒa
23,904×(max) 8 nodesr2ΥW → ΣKΒ6 → ΜgfC → z0ΧO → Χal2 → ΥAΜ4 → ΠΑL8 → ΘehG
23,783×(max) 8 nodesJEΘΕ → tkbU → P8Ξy → ΖYnI → nEΘa → tCΚU → xOxQ → ZWpo
23,664×(max) 8 nodesV2Υs → ΣMz6 → ΜcjC → z6ΠO → ΚalE → vAΜS → ΒStM → fQvi
23,656×(max) 8 nodesX2Υq → ΣIΔ6 → ΜkbC → z8ΞO → ΖalI → nAΜa → ΒCΚM → xehQ
23,632×(max) 8 nodeshGΖg → p0ΧY → ΧGΖ2 → ΥoX4 → ΠGΖ8 → ΘoXG → rGΖW → pKΒY
23,624×(max) 8 nodesdKΒk → h6Πg → Κ0ΧE → ΧuR2 → ΥSt4 → ΠQv8 → ΘUrG → rMzW
23,608×(max) 8 nodesfAΜi → Β2ΥM → Σeh6 → Μ2ΥC → ΣyN6 → ΜalC → zAΜO → ΒalM
23,600×(max) 8 nodesjAΜe → Β4ΣM → ΞehA → Δ2ΥK → Σid6 → Μ4ΣC → ΞyNA → ΔalK
23,553×(max) 8 nodesTQvu → VQvs → VMzs → dMzk → d6Πk → Κ6ΠE → ΚuRE → vStS
23,547×(max) 8 nodesFCΚΙ → xsTQ → XOxq → ZIΔo → lEΘc → t8ΞU → ΖOxI → nYna
23,506×(max) 8 nodes96ΠΟ → ΚΕHE → vmZS → TCΚu → xQvQ → XUrq → NIΔΑ → lcjc
23,455×(max) 8 nodesHCΚΗ → xoXQ → XGΖq → pIΔY → lGΖc → p8ΞY → ΖGΖI → pmZY
23,320×(max) 8 nodesb8Ξm → ΖAΜI → ΒmZM → fCΚi → x2ΥQ → ΣWp6 → ΜIΔC → zkbO
23,304×(max) 8 nodesZKΒo → hEΘg → t0ΧU → ΧOx2 → ΥYn4 → ΠEΘ8 → ΘsTG → rOxW
23,304×(max) 8 nodesZ0Χo → ΧEΘ2 → ΥsT4 → ΠOx8 → ΘYnG → rEΘW → tKΒU → hOxg
23,288×(max) 8 nodesL6ΠΓ → ΚgfE → v0ΧS → ΧSt2 → ΥQv4 → ΠUr8 → ΘMzG → rcjW
23,280×(max) 8 nodesh8Ξg → Ζ0ΧI → ΧmZ2 → ΥCΚ4 → ΠwP8 → ΘWpG → rIΔW → lKΒc
23,255×(max) 8 nodesNEΘΑ → tcjU → P6Πy → ΚYnE → vEΘS → tStU → ROxw → ZUro
23,247×(max) 8 nodesH8ΞΗ → ΖoXI → nGΖa → pCΚY → xGΖQ → pWpY → JGΖΕ → pkbY
23,032×(max) 8 nodesXIΔq → lIΔc → l8Ξc → Ζ8ΞI → ΖmZI → nCΚa → xCΚQ → xWpQ
23,009×(max) 8 nodesFAΜΙ → ΒsTM → fOxi → Z2Υo → ΣEΘ6 → ΜsTC → zOxO → bYnm
23,008×(max) 8 nodesPAΜy → ΒYnM → fEΘi → t2ΥU → ΣOx6 → ΜYnC → zEΘO → talU
22,984×(max) 8 nodesbIΔm → lAΜc → Β8ΞM → ΖehI → n2Υa → ΣCΚ6 → ΜwPC → zWpO
22,984×(max) 8 nodesN4ΣΑ → ΞcjA → Δ6ΠK → ΚidE → v4ΣS → ΞStA → ΔQvK → jUre
22,976×(max) 8 nodesX4Σq → ΞIΔA → ΔkbK → j8Ξe → Ζ4ΣI → ΞmZA → ΔCΚK → xidQ
22,952×(max) 8 nodesR0Χw → ΧUr2 → ΥMz4 → Πcj8 → Θ6ΠG → ΚqVE → vKΒS → hStg
22,931×(max) 8 nodesB6ΠΝ → ΚΑLE → vehS → T2Υu → ΣQv6 → ΜUrC → zMzO → dalk
22,928×(max) 8 nodesf4Σi → Ξ2ΥA → ΣΓJ6 → ΜidC → z4ΣO → ΞalA → ΔAΜK → ΒidM
22,923×(max) 8 nodes94ΣΟ → ΞΕHA → ΔmZK → jCΚe → x4ΣQ → ΞWpA → ΔIΔK → lidc
22,856×(max) 8 nodesr0ΧW → ΧKΒ2 → Υgf4 → Π0Χ8 → ΧΗF2 → ΥqV4 → ΠKΒ8 → ΘgfG
22,854×(max) 8 nodes30ΧΦ → ΧΡ52 → ΥΛB4 → ΠyN8 → ΘalG → rAΜW → ΒKΒM → hehg
22,721×(max) 8 nodesJAΜΕ → ΒkbM → f8Ξi → Ζ2ΥI → ΣmZ6 → ΜCΚC → zwPO → bWpm
22,704×(max) 8 nodesR8Ξw → ΖUrI → nMza → dCΚk → x6ΠQ → ΚWpE → vIΔS → lStc
22,648×(max) 8 nodesV4Σs → ΞMzA → ΔcjK → j6Πe → Κ4ΣE → ΞuRA → ΔStK → jQve
22,560×(max) 8 nodesb0Χm → ΧAΜ2 → ΥΑL4 → Πeh8 → Θ2ΥG → ΣqV6 → ΜKΒC → zgfO
22,459×(max) 8 nodesF0ΧΙ → ΧsT2 → ΥOx4 → ΠYn8 → ΘEΘG → tqVU → PKΒy → hYng
22,421×(max) 8 nodesTOxu → ZQvo → VEΘs → tMzU → dOxk → Z6Πo → ΚEΘE → vsTS
22,255×(max) 8 nodesN8ΞΑ → ΖcjI → n6Πa → ΚCΚE → xuRQ → XStq → RIΔw → lUrc
22,241×(max) 8 nodesH0ΧΗ → ΧoX2 → ΥGΖ4 → ΠoX8 → ΘGΖG → roXW → LGΖΓ → pgfY
21,843×(max) 8 nodesB2ΥΝ → ΣΑL6 → ΜehC → z2ΥO → Σal6 → ΜAΜC → ΒyNM → fali
21,819×(max) 8 nodesTKΒu → hQvg → V0Χs → ΧMz2 → Υcj4 → Π6Π8 → ΚΗFE → vqVS
21,696×(max) 8 nodesVIΔs → lMzc → d8Ξk → Ζ6ΠI → ΚmZE → vCΚS → xStQ → XQvq
21,665×(max) 8 nodesLCΚΓ → xgfQ → X0Χq → ΧIΔ2 → Υkb4 → Π8Ξ8 → ΘΕHG → rmZW
21,648×(max) 8 nodesR2Υw → ΣUr6 → ΜMzC → zcjO → b6Πm → ΚAΜE → ΒuRM → fSti
21,640×(max) 8 nodesbCΚm → xAΜQ → ΒWpM → fIΔi → l2Υc → Σ8Ξ6 → ΜΕHC → zmZO
21,600×(max) 8 nodesL8ΞΓ → ΖgfI → n0Χa → ΧCΚ2 → ΥwP4 → ΠWp8 → ΘIΔG → rkbW
21,574×(max) 8 nodes52ΥΤ → ΣΝ96 → ΜΓJC → zidO → b4Σm → ΞAΜA → ΔΑLK → jehe
21,312×(max) 8 nodesNAΜΑ → ΒcjM → f6Πi → Κ2ΥE → ΣuR6 → ΜStC → zQvO → bUrm
21,304×(max) 8 nodesT4Σu → ΞQvA → ΔUrK → jMze → d4Σk → Ξ6ΠA → ΚΓJE → vidS
21,253×(max) 8 nodesF6ΠΙ → ΚsTE → vOxS → ZSto → REΘw → tUrU → PMzy → dYnk
21,207×(max) 8 nodesD4ΣΛ → ΞwPA → ΔWpK → jIΔe → l4Σc → Ξ8ΞA → ΖΓJI → nida
21,147×(max) 8 nodes70ΧΡ → ΧΙD2 → ΥuR4 → ΠSt8 → ΘQvG → rUrW → NKΒΑ → hcjg
21,089×(max) 8 nodesDAΜΛ → ΒwPM → fWpi → J2ΥΕ → Σkb6 → Μ8ΞC → ΖyNI → nala
21,048×(max) 8 nodesTEΘu → tQvU → VOxs → ZMzo → dEΘk → t6ΠU → ΚOxE → vYnS
21,040×(max) 8 nodesTGΖu → pQvY → VGΖs → pMzY → dGΖk → p6ΠY → ΚGΖE → voXS
20,992×(max) 8 nodesP2Υy → ΣYn6 → ΜEΘC → zsTO → bOxm → ZAΜo → ΒEΘM → tehU
20,984×(max) 8 nodesHAΜΗ → ΒoXM → fGΖi → p2ΥY → ΣGΖ6 → ΜoXC → zGΖO → palY
20,960×(max) 8 nodesJ4ΣΕ → ΞkbA → Δ8ΞK → ΖidI → n4Σa → ΞCΚA → ΔwPK → jWpe
20,939×(max) 8 nodes74ΣΡ → ΞΙDA → ΔuRK → jSte → R4Σw → ΞUrA → ΔMzK → jcje
20,928×(max) 8 nodesD0ΧΛ → ΧwP2 → ΥWp4 → ΠIΔ8 → ΘkbG → r8ΞW → ΖKΒI → ngfa
20,928×(max) 8 nodesXKΒq → hIΔg → l0Χc → Χ8Ξ2 → ΥΕH4 → ΠmZ8 → ΘCΚG → xqVQ
20,872×(max) 8 nodesj0Χe → Χ4Σ2 → ΥΝ94 → ΠΓJ8 → ΘidG → r4ΣW → ΞKΒA → ΔgfK
20,801×(max) 8 nodes90ΧΟ → ΧΕH2 → ΥmZ4 → ΠCΚ8 → ΘwPG → rWpW → LIΔΓ → lgfc
20,711×(max) 8 nodesB8ΞΝ → ΖΑLI → neha → D2ΥΛ → ΣwP6 → ΜWpC → zIΔO → lalc
20,704×(max) 8 nodesPCΚy → xYnQ → XEΘq → tIΔU → lOxc → Z8Ξo → ΖEΘI → tmZU
20,696×(max) 8 nodesT6Πu → ΚQvE → vUrS → TMzu → dQvk → V6Πs → ΚMzE → vcjS
20,688×(max) 8 nodesJ6ΠΕ → ΚkbE → v8ΞS → ΖStI → nQva → VCΚs → xMzQ → dWpk
20,688×(max) 8 nodesRCΚw → xUrQ → XMzq → dIΔk → l6Πc → Κ8ΞE → ΖuRI → nSta
20,680×(max) 8 nodesJ8ΞΕ → ΖkbI → n8Ξa → ΖCΚI → xmZQ → XCΚq → xIΔQ → lWpc
20,656×(max) 8 nodesF2ΥΙ → ΣsT6 → ΜOxC → zYnO → bEΘm → tAΜU → ΒOxM → fYni
20,653×(max) 8 nodesRAΜw → ΒUrM → fMzi → d2Υk → Σ6Π6 → ΜΙDC → zuRO → bStm
20,648×(max) 8 nodesH2ΥΗ → ΣoX6 → ΜGΖC → zoXO → bGΖm → pAΜY → ΒGΖM → pehY
20,616×(max) 8 nodesLEΘΓ → tgfU → P0Χy → ΧYn2 → ΥEΘ4 → ΠsT8 → ΘOxG → rYnW
20,584×(max) 8 nodesbAΜm → ΒAΜM → ΒehM → f2Υi → Σ2Υ6 → ΣΛB6 → ΜyNC → zalO
20,577×(max) 8 nodes50ΧΤ → ΧΝ92 → ΥΓJ4 → Πid8 → Θ4ΣG → ΞqVA → ΔKΒK → jgfe
20,544×(max) 8 nodesfKΒi → h2Υg → Σ0Χ6 → ΧΛB2 → ΥyN4 → Πal8 → ΘAΜG → ΒqVM
20,544×(max) 8 nodesL2ΥΓ → Σgf6 → Μ0ΧC → ΧyN2 → Υal4 → ΠAΜ8 → ΘΑLG → rehW
20,536×(max) 8 nodesh4Σg → Ξ0ΧA → ΧΓJ2 → Υid4 → Π4Σ8 → ΞΗFA → ΔqVK → jKΒe
20,525×(max) 8 nodesD8ΞΛ → ΖwPI → nWpa → JCΚΕ → xkbQ → X8Ξq → ΖIΔI → nkba
20,509×(max) 8 nodes72ΥΡ → ΣΙD6 → ΜuRC → zStO → bQvm → VAΜs → ΒMzM → fcji
20,352×(max) 8 nodesNCΚΑ → xcjQ → X6Πq → ΚIΔE → vkbS → T8Ξu → ΖQvI → nUra
20,304×(max) 8 nodesN2ΥΑ → Σcj6 → Μ6ΠC → ΚyNE → valS → TAΜu → ΒQvM → fUri
20,264×(max) 8 nodesVKΒs → hMzg → d0Χk → Χ6Π2 → ΥΙD4 → ΠuR8 → ΘStG → rQvW
20,256×(max) 8 nodesJ0ΧΕ → Χkb2 → Υ8Ξ4 → ΠΕH8 → ΘmZG → rCΚW → xKΒQ → hWpg
20,251×(max) 8 nodesbKΒm → hAΜg → Β0ΧM → Χeh2 → Υ2Υ4 → ΣΟ76 → ΜΗFC → zqVO
20,129×(max) 8 nodesL4ΣΓ → ΞgfA → Δ0ΧK → Χid2 → Υ4Σ4 → ΠΝ98 → ΘΓJG → ridW
19,576×(max) 8 nodesh0Χg → Χ0Χ2 → ΧΤ32 → ΥΟ74 → ΠΗF8 → ΘqVG → rKΒW → hKΒg
18,688×(max) 8 nodesF8ΞΙ → ΖsTI → nOxa → ZCΚo → xEΘQ → tWpU → PIΔy → lYnc
18,616×(max) 8 nodes92ΥΟ → ΣΕH6 → ΜmZC → zCΚO → xalQ → XAΜq → ΒIΔM → lehc
18,584×(max) 8 nodesN0ΧΑ → Χcj2 → Υ6Π4 → ΠΙD8 → ΘuRG → rStW → RKΒw → hUrg
18,367×(max) 8 nodesB4ΣΝ → ΞΑLA → ΔehK → j2Υe → Σ4Σ6 → ΞΛBA → ΔyNK → jale
18,352×(max) 8 nodesH6ΠΗ → ΚoXE → vGΖS → pStY → RGΖw → pUrY → NGΖΑ → pcjY
18,336×(max) 8 nodesD6ΠΛ → ΚwPE → vWpS → TIΔu → lQvc → V8Ξs → ΖMzI → ncja
18,192×(max) 8 nodesB0ΧΝ → ΧΑL2 → Υeh4 → Π2Υ8 → ΣΗF6 → ΜqVC → zKΒO → halg
18,152×(max) 8 nodesL0ΧΓ → Χgf2 → Υ0Χ4 → ΧΟ72 → ΥΗF4 → ΠqV8 → ΘKΒG → rgfW
17,333×(max) 8 nodesLAΜΓ → ΒgfM → f0Χi → Χ2Υ2 → ΥΡ54 → ΠΛB8 → ΘyNG → ralW
12,340×4 nodesjEΘe → t4ΣU → ΞOxA → ΔYnK
12,188×4 nodeslCΚc → x8ΞQ → ΖWpI → nIΔa
12,100×4 nodesΘ0ΧG → ΧqV2 → ΥKΒ4 → Πgf8
11,885×4 nodesHEΘΗ → toXU → PGΖy → pYnY
11,664×4 nodesjGΖe → p4ΣY → ΞGΖA → ΔoXK
11,368×4 nodesZGΖo → pEΘY → tGΖU → pOxY
10,700×4 nodesZEΘo → tEΘU → tOxU → ZOxo
10,660×4 nodesP4Σy → ΞYnA → ΔEΘK → tidU
10,660×4 nodesZ4Σo → ΞEΘA → ΔsTK → jOxe
10,620×4 nodesj4Σe → Ξ4ΣA → ΞΓJA → ΔidK
10,516×4 nodesR6Πw → ΚUrE → vMzS → dStk
10,460×4 nodesb2Υm → ΣAΜ6 → ΜΑLC → zehO
9,312×4 nodesH4ΣΗ → ΞoXA → ΔGΖK → pidY
8,980×4 nodesF4ΣΙ → ΞsTA → ΔOxK → jYne
6,150×2 nodesΔ4ΣK → ΞidA
4,510×2 nodesPEΘy → tYnU
3,009×(fixed) 1 node pGΖY
52 cycles27,587,496×3 nodesuQΨvT → wRΨuR → vUΨrS
13,920,061×(max) 4 nodesuRΨuT → vQΨvS → wSΨtR → vTΨsS
610 cycles239,462,322×(max) 49 nodesL60ΧΡΓ → ΧΛgfC2 → Υy0ΧO4 → ΧΠZm72 → ΥΙCΚE4 → ΠxtSP8 → ΘYQvoG → rVFΗrW → rMKΒΑW → heKΒig → h40ΧΤg → ΧΟ0Χ82 → ΧΥΖG32 → ΥΡoX64 → ΠΛGΖC8 → ΘyoXOG → raGΖmW → pLBΛΒY → zgGΖgO → paΨΨlY → om3ΤaZ → ΠFBΛΘ8 → ΘzrUNG → rcMzkW → dL7ΟΒk → Θg6ΠgG → ΚqΨΨVE → ΙrIΔVF → tlLΑbU → fP9Νxi → ΔY2ΥoK → ΣjFΗd6 → Μr5ΡVC → ΜzLΑNC → zfbkhO → b91ΦΞm → ΥΕAΜI4 → ΠΒlaL8 → ΘgAΜgG → ΒqΨΨVM → ΑrAΜVN → ΒdLΑjM → ge5Ρih → Μ40ΧΤC → ΧΟyN82 → ΥΗalG4 → ΠqAΜW8 → ΘΒJΓLG → rjfgdW
187,768,435×46 nodesjX5Ρpe → ΜI4ΣΕC → ΞzlaNA → ΔcAΜkK → Βj7ΟdM → Θf5ΡhG → Μr1ΦVC → ΥzLΑN4 → Πfbkh8 → Θ91ΦΞG → ΥΕqVI4 → ΠmKΒa8 → ΘhBΛfG → zr1ΦVO → ΥbLΑl4 → Πf9Νh8 → ΘΔ1ΦJG → ΥrjcV4 → ΠM6ΠΑ8 → ΚΘdiFE → vs4ΣUS → ΞTNytA → ΔbPwlK → jX9Νpe → ΔI4ΣΕK → ΞmidaA → ΔC4ΣΛK → ΞyidOA → Δa4ΣmK → ΞjBΛdA → Δz5ΡNK → ΜjbkdC → z95ΡΞO → ΜΕalIC → zmAΜaO → ΒbBΛlM → zf9ΝhO → Δb1ΦlK → Υj9Νd4 → ΠΔ5ΡJ8 → ΜΘjcFC → zs6ΠUO → ΚbNylE → vb9ΝlS → ΔT9ΝtK → ΔjPwdK
153,018,097×42 nodesXD5ΡΚq → ΜwIΔQC → zlVqbO → bL9ΝΒm → ΔgAΜgK → ΒiΨΨdM → ΑjIΔdN → ld5Ρjc → Μ95ΡΞC → ΜΕyNIC → zmalaO → bCAΜΛm → ΒyAΜOM → ΒfZmhM → fD1ΦΚi → Υw2ΥQ4 → ΣΠVq76 → ΜΙKΒEC → zugfSO → bS0Χum → ΧSAΜu2 → ΥΒRuL4 → ΠgStg8 → ΘQΨΨvG → ΗwBΛQH → zpVqXO → bLHΕΒm → ngAΜga → ΒCΨΨΚM → ΛΑ7ΟMD → ΘxdiPG → rY4ΣoW → ΞLFΗΒA → ΔrfgVK → jM0ΧΑe → Χe4Σi2 → ΥΞ3Τ94 → ΡΟΔI87 → ΚΗkbGE → vq8ΞWS → ΖTJΓtI → njPwda
17,003,736×7 nodesvj9ΝdS → ΔT5ΡtK → ΜjPwdC → zX5ΡpO → ΜbHΕlC → zn9ΝZO → ΔbDΙlK
15,407,872×7 nodesvr1ΦVS → ΥTLΑt4 → ΠfPwh8 → ΘX1ΦpG → ΥrHΕV4 → ΠnLΑZ8 → ΘfDΙhG
7,122,103×23 nodesXPHΕxq → nYIΔoa → lGCΚΗc → xq8ΞWQ → ΖXJΓpI → njHΕda → nD5ΡΚa → ΜwCΚQC → zxVqPO → bYKΒom → hGAΜΗg → Βq0ΧWM → ΧfJΓh2 → Υj1Φd4 → ΥΠ5Ρ74 → ΠΜΘEB8 → ΘΑsTMG → reOxiW → ZL3ΤΒo → ΠgEΘg8 → ΘsΨΨTG → ΗtEΘTH → tpPwXU
2,680,813×13 nodesXL9ΝΒq → ΔgIΔgK → liΨΨdc → kj2Υdd → Σ75ΡΠ6 → ΝΛΘECB → ΒysTOM → faOxmi → ZC2ΥΛo → ΣyEΘO6 → ΜtZmTC → zQCΚwO → xbVqlQ
70,602×4 nodesZSGΖuo → pSEΘuY → tSGΖuU → pSOxuY
60,080×4 nodesZSEΘuo → tSEΘuU → tSOxuU → ZSOxuo
20,485×(fixed) 1 node pSGΖuY
73 cycles6,639,153,672×2 nodesΒhKΨΒfM → ΓfLΨΑhL
746,810,030×2 nodesΓhJΨΓfL → ΔhMΨzfK
708,026,403×(max) 4 nodesΑfJΨΓhN → ΔfKΨΒhK → ΓjLΨΑdL → ΒhMΨzfM
8+---Not showing digit sets 8+ due to verbosity.