Base 103: 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 4,896×(max) 6 nodes7κ → βF → ΚV → dΒ → NΣ → tl
31 cycle 187,357×(max) 2 nodesoρq → pρp
425 cycles201,475×(max) 51 nodesB2ξη → μΤL6 → ζwhC → ΣEβO → ΜslU → h6κy → δGΩE → ΞΗXS → lYΖu → X8θΙ → ΩaΔI → ΖSΜa → jUΚw → fCδΑ → ΠKΥQ → zopg → J0πΨ → πΓb2 → ξQΞ4 → κmr8 → β4μG → θΙVA → ΧcΒK → ΒOΠe → rMΣo → v2ξk → μAζ6 → ζΤLC → ΣwhO → tEβm → Μ6κU → δgxE → ΞGΩS → ΘktY → Z8θΗ → ΩWΘI → ΖaΔa → VSΜΛ → jezw → LCδΦ → ΠyfQ → pIΧq → Δ0πc → πQΞ2 → ξmr4 → κ4μ8 → θαFA → ΧΙVK → ΒcΒe → PMΣΡ → vqnk
201,359×(max) 51 nodesLIΧΦ → Δyfc → RIΧΟ → Δmrc → R4μΟ → θmrA → Χ4μK → θΑdA → ΧMΣK → Βuje → NAζΤ → ΥujM → xAζi → ΥEβM → ΜwhU → hEβy → ΜGΩU → ΘgxY → ZGΩΗ → ΘWΘY → bYΖΕ → XSΜΙ → jaΔw → TCδΝ → ΠivQ → pCδq → Π0πQ → πop2 → ξ0π4 → πι72 → ξαF4 → κΙV8 → βcΒG → ΚOΠW → rcΒo → P2ξΡ → μqn6 → ζ2ξC → μΡN6 → ζslC → Σ6κO → δslE → Ξ6κS → δktE → Ξ8θS → ΩktI → Ζ8θa → ΩUΚI → Ζeza → VKΥΛ → zezg
201,335×(max) 51 nodesFCδγ → ΠΛTQ → pgxq → H0πα → πΗX2 → ξYΖ4 → κWΘ8 → βaΔG → ΚSΜW → jcΒw → PCδΡ → ΠqnQ → p2ξq → μ0π6 → πεB2 → ξΡN4 → κsl8 → β6κG → δΙVE → ΞcΒS → lOΠu → r8θo → Ω2ξI → μΕZ6 → ζUΚC → ΣezO → tKΥm → z6κg → δIΧE → ΞΓbS → lQΞu → n8θs → Ω4μI → θΕZA → ΧUΚK → Βeze → NKΥΤ → zujg → JAζΨ → ΥΓbM → xQΞi → nEβs → Μ4μU → θgxA → ΧGΩK → ΘΑdY → ZMΣΗ → vWΘk → bAζΕ → ΥSΜM → xivi
201,235×(max) 51 nodesB0πη → πΤL2 → ξwh4 → κEβ8 → βΛTG → ΚgxW → dGΩΓ → ΘOΠY → rYΖo → X2ξΙ → μaΔ6 → ζSΜC → ΣivO → tCδm → Π6κQ → δopE → Ξ0πS → πkt2 → ξ8θ4 → κΨH8 → βΕZG → ΚUΚW → fcΒΑ → PKΥΡ → zqng → J2ξΨ → μΓb6 → ζQΞC → ΣmrO → t4μm → θ6κA → δΦJE → ΞΑdS → lMΣu → v8θk → ΩAζI → ΥΕZM → xUΚi → fEβΑ → ΜKΥU → zgxg → JGΩΨ → ΘΓbY → ZQΞΗ → nWΘs → b4μΕ → θSΜA → ΧivK → ΒCδe → ΠMΣQ → vopk
201,011×(max) 51 nodes52ξν → μη96 → ζΦJC → ΣΑdO → tMΣm → v6κk → δAζE → ΥΝRM → xkti → F8θγ → ΩΛTI → Ζgxa → VGΩΛ → ΘezY → ZKΥΗ → zWΘg → bIΧΕ → ΔSΜc → jQΞw → nCδs → Π4μQ → θopA → Χ0πK → πΑd2 → ξMΣ4 → κuj8 → βAζG → ΥΙVM → xcΒi → PEβΡ → ΜqnU → h2ξy → μGΩ6 → ζΗXC → ΣYΖO → tWΘm → b6κΕ → δSΜE → ΞivS → lCδu → Π8θQ → ΩopI → Ζ0πa → πUΚ2 → ξez4 → κKΥ8 → βyfG → ΚIΧW → ΔcΒc → ROΠΟ → rmro
200,371×(max) 51 nodesD0πε → πΟP2 → ξop4 → κ0π8 → παF2 → ξΙV4 → κcΒ8 → βOΠG → ΚqnW → d2ξΓ → μOΠ6 → ζqnC → Σ2ξO → μsl6 → ζ6κC → δΡNE → ΞslS → l6κu → δ8θE → ΩΝRI → Ζkta → V8θΛ → ΩezI → ΖKΥa → zUΚg → fIΧΑ → ΔKΥc → zQΞg → nIΧs → Δ4μc → θQΞA → ΧmrK → Β4μe → θMΣA → ΧujK → ΒAζe → ΥMΣM → xuji → FAζγ → ΥΛTM → xgxi → HEβα → ΜΗXU → hYΖy → XGΩΙ → ΘaΔY → ZSΜΗ → jWΘw → bCδΕ → ΠSΜQ → pivq
200,243×(max) 51 nodes30πο → πλ52 → ξεB4 → κΡN8 → βslG → Κ6κW → δcΒE → ΞOΠS → rkto → 92ξι → μΨH6 → ζΕZC → ΣUΚO → tezm → L6κΦ → δyfE → ΞIΧS → Δktc → R8θΟ → ΩmrI → Ζ4μa → θUΚA → ΧezK → ΒKΥe → zMΣg → vIΧk → ΔAζc → ΥQΞM → xmri → F4μγ → θΛTA → ΧgxK → ΒGΩe → ΘMΣY → vYΖk → XAζΙ → ΥaΔM → xSΜi → jEβw → ΜCδU → ΠgxQ → pGΩq → Θ0πY → πYΖ2 → ξWΘ4 → κaΔ8 → βSΜG → ΚivW → dCδΓ → ΠOΠQ → ropo
200,195×(max) 51 nodesB6κη → δΤLE → ΞwhS → lEβu → Μ8θU → ΩgxI → ΖGΩa → ΘUΚY → fYΖΑ → XKΥΙ → zaΔg → TIΧΝ → Δivc → RCδΟ → ΠmrQ → p4μq → θ0πA → πΦJ2 → ξΑd4 → κMΣ8 → βujG → ΚAζW → ΥcΒM → xOΠi → rEβo → Μ2ξU → μgx6 → ζGΩC → ΣΗXO → tYΖm → X6κΙ → δaΔE → ΞSΜS → livu → D8θε → ΩΟPI → Ζopa → V0πΛ → πez2 → ξKΥ4 → κyf8 → βIΧG → ΚΓbW → dQΞΓ → nOΠs → r4μo → θ2ξA → μΦJ6 → ζΑdC → ΣMΣO → vslk
200,143×(max) 51 nodesDAζε → ΥΟPM → xopi → F0πγ → πΛT2 → ξgx4 → κGΩ8 → βΗXG → ΚYΖW → dWΘΓ → bOΠΕ → rSΜo → j2ξw → μCδ6 → ζΟPC → ΣopO → t0πm → π6κ2 → ξγD4 → κΝR8 → βktG → Κ8θW → ΩcΒI → ΖOΠa → rUΚo → f2ξΑ → μKΥ6 → ζyfC → ΣIΧO → Δslc → R6κΟ → δmrE → Ξ4μS → θktA → Χ8θK → ΩΑdI → ΖMΣa → vUΚk → fAζΑ → ΥKΥM → zwhg → JEβΨ → ΜΓbU → hQΞy → nGΩs → Θ4μY → θYΖA → ΧWΘK → ΒaΔe → TMΣΝ → vivk
199,155×(max) 51 nodesH8θα → ΩΗXI → ΖYΖa → XUΚΙ → faΔΑ → TKΥΝ → zivg → JCδΨ → ΠΓbQ → pQΞq → n0πs → π4μ2 → ξη94 → κΦJ8 → βΑdG → ΚMΣW → vcΒk → PAζΡ → ΥqnM → x2ξi → μEβ6 → ζΛTC → ΣgxO → tGΩm → Θ6κY → δYΖE → ΞWΘS → laΔu → T8θΝ → ΩivI → ΖCδa → ΠUΚQ → pezq → L0πΦ → πyf2 → ξIΧ4 → κΓb8 → βQΞG → ΚmrW → d4μΓ → θOΠA → ΧqnK → Β2ξe → μMΣ6 → ζujC → ΣAζO → ΥslM → x6κi → δEβE → ΞΛTS → lgxu
199,155×(max) 51 nodes50πν → πη92 → ξΦJ4 → κΑd8 → βMΣG → ΚujW → dAζΓ → ΥOΠM → xqni → F2ξγ → μΛT6 → ζgxC → ΣGΩO → ΘslY → Z6κΗ → δWΘE → ΞaΔS → lSΜu → j8θw → ΩCδI → ΠΕZQ → pUΚq → f0πΑ → πKΥ2 → ξyf4 → κIΧ8 → βΓbG → ΚQΞW → ncΒs → P4μΡ → θqnA → Χ2ξK → μΑd6 → ζMΣC → ΣujO → tAζm → Υ6κM → δwhE → ΞEβS → ΜktU → h8θy → ΩGΩI → ΘΕZY → ZUΚΗ → fWΘΑ → bKΥΕ → zSΜg → jIΧw → ΔCδc → ΠQΞQ → pmrq
199,123×(max) 51 nodesB8θη → ΩΤLI → Ζwha → VEβΛ → ΜezU → hKΥy → zGΩg → ΘIΧY → ΔYΖc → XQΞΙ → naΔs → T4μΝ → θivA → ΧCδK → ΠΑdQ → pMΣq → v0πk → πAζ2 → ξΤL4 → κwh8 → βEβG → ΜΙVU → hcΒy → PGΩΡ → ΘqnY → Z2ξΗ → μWΘ6 → ζaΔC → ΣSΜO → tivm → D6κε → δΟPE → ΞopS → l0πu → π8θ2 → ξΨH4 → κΕZ8 → βUΚG → ΚezW → dKΥΓ → zOΠg → rIΧo → Δ2ξc → μQΞ6 → ζmrC → Σ4μO → θslA → Χ6κK → δΑdE → ΞMΣS → vktk
199,067×(max) 51 nodesZWΘΗ → bWΘΕ → bSΜΕ → jSΜw → jCδw → ΠCδQ → ΠopQ → p0πq → π0π2 → πν32 → ξι74 → καF8 → βΙVG → ΚcΒW → dOΠΓ → rOΠo → r2ξo → μ2ξ6 → μεB6 → ζΡNC → ΣslO → t6κm → δ6κE → δΝRE → ΞktS → l8θu → Ω8θI → ΩΕZI → ΖUΚa → fUΚΑ → fKΥΑ → zKΥg → zIΧg → ΔIΧc → ΔQΞc → nQΞs → n4μs → θ4μA → θΦJA → ΧΑdK → ΒMΣe → vMΣk → vAζk → ΥAζM → ΥwhM → xEβi → ΜEβU → ΜgxU → hGΩy → ΘGΩY → ΘYΖY
198,739×(max) 51 nodes90πι → πΨH2 → ξΕZ4 → κUΚ8 → βezG → ΚKΥW → zcΒg → PIΧΡ → Δqnc → R2ξΟ → μmr6 → ζ4μC → θΡNA → ΧslK → Β6κe → δMΣE → ΞujS → lAζu → Υ8θM → ΩwhI → ΖEβa → ΜUΚU → hezy → LGΩΦ → ΘyfY → ZIΧΗ → ΔWΘc → bQΞΕ → nSΜs → j4μw → θCδA → ΧΟPK → Βope → N0πΤ → πuj2 → ξAζ4 → κΤL8 → βwhG → ΚEβW → ΜcΒU → hOΠy → rGΩo → Θ2ξY → μYΖ6 → ζWΘC → ΣaΔO → tSΜm → j6κw → δCδE → ΠΝRQ → pktq
198,451×(max) 51 nodesB4μη → θΤLA → ΧwhK → ΒEβe → ΜMΣU → vgxk → HAζα → ΥΗXM → xYΖi → XEβΙ → ΜaΔU → hSΜy → jGΩw → ΘCδY → ΠYΖQ → pWΘq → b0πΕ → πSΜ2 → ξiv4 → κCδ8 → βΟPG → ΚopW → d0πΓ → πOΠ2 → ξqn4 → κ2ξ8 → μαF6 → ζΙVC → ΣcΒO → tOΠm → r6κo → δ2ξE → μΝR6 → ζktC → Σ8θO → ΩslI → Ζ6κa → δUΚE → ΞezS → lKΥu → z8θg → ΩIΧI → ΖΓba → VQΞΛ → nezs → L4μΦ → θyfA → ΧIΧK → ΔΑdc → RMΣΟ → vmrk
197,987×(max) 51 nodesD2ξε → μΟP6 → ζopC → Σ0πO → πsl2 → ξ6κ4 → κγD8 → βΝRG → ΚktW → d8θΓ → ΩOΠI → Ζqna → V2ξΛ → μez6 → ζKΥC → ΣyfO → tIΧm → Δ6κc → δQΞE → ΞmrS → l4μu → θ8θA → ΩΦJI → ΖΑda → VMΣΛ → vezk → LAζΦ → ΥyfM → xIΧi → ΔEβc → ΜQΞU → ngxs → H4μα → θΗXA → ΧYΖK → ΒWΘe → bMΣΕ → vSΜk → jAζw → ΥCδM → ΠwhQ → pEβq → Μ0πU → πgx2 → ξGΩ4 → κΗX8 → βYΖG → ΚWΘW → daΔΓ → TOΠΝ → rivo
197,575×(max) 51 nodes72ξλ → μγD6 → ζΝRC → ΣktO → t8θm → Ω6κI → δΕZE → ΞUΚS → lezu → L8θΦ → ΩyfI → ΖIΧa → ΔUΚc → fQΞΑ → nKΥs → z4μg → θIΧA → ΧΓbK → ΒQΞe → nMΣs → v4μk → θAζA → ΧΤLK → Βwhe → NEβΤ → ΜujU → hAζy → ΥGΩM → ΘwhY → ZEβΗ → ΜWΘU → haΔy → TGΩΝ → ΘivY → ZCδΗ → ΠWΘQ → paΔq → T0πΝ → πiv2 → ξCδ4 → κΟP8 → βopG → Κ0πW → πcΒ2 → ξOΠ4 → κqn8 → β2ξG → μΙV6 → ζcΒC → ΣOΠO → tqnm
197,495×(max) 51 nodes74μλ → θγDA → ΧΝRK → Βkte → N8θΤ → ΩujI → ΖAζa → ΥUΚM → xezi → LEβΦ → ΜyfU → hIΧy → ΔGΩc → ΘQΞY → nYΖs → X4μΙ → θaΔA → ΧSΜK → Βive → NCδΤ → ΠujQ → pAζq → Υ0πM → πwh2 → ξEβ4 → κΛT8 → βgxG → ΚGΩW → ΘcΒY → ZOΠΗ → rWΘo → b2ξΕ → μSΜ6 → ζivC → ΣCδO → ΠslQ → p6κq → δ0πE → πΝR2 → ξkt4 → κ8θ8 → βΨHG → ΚΕZW → dUΚΓ → fOΠΑ → rKΥo → z2ξg → μIΧ6 → ζΓbC → ΣQΞO → tmrm
197,167×(max) 51 nodes94μι → θΨHA → ΧΕZK → ΒUΚe → fMΣΑ → vKΥk → zAζg → ΥIΧM → Δwhc → REβΟ → ΜmrU → h4μy → θGΩA → ΧΗXK → ΒYΖe → XMΣΙ → vaΔk → TAζΝ → ΥivM → xCδi → ΠEβQ → ΜopU → h0πy → πGΩ2 → ξΗX4 → κYΖ8 → βWΘG → ΚaΔW → dSΜΓ → jOΠw → rCδo → Π2ξQ → μop6 → ζ0πC → πΡN2 → ξsl4 → κ6κ8 → δαFE → ΞΙVS → lcΒu → P8θΡ → ΩqnI → Ζ2ξa → μUΚ6 → ζezC → ΣKΥO → zslg → J6κΨ → δΓbE → ΞQΞS → nkts
197,135×(max) 51 nodesD4με → θΟPA → ΧopK → Β0πe → πMΣ2 → ξuj4 → κAζ8 → βΤLG → ΚwhW → dEβΓ → ΜOΠU → rgxo → H2ξα → μΗX6 → ζYΖC → ΣWΘO → taΔm → T6κΝ → δivE → ΞCδS → ΠktQ → p8θq → Ω0πI → πΕZ2 → ξUΚ4 → κez8 → βKΥG → ΚyfW → dIΧΓ → ΔOΠc → rQΞo → n2ξs → μ4μ6 → θεBA → ΧΡNK → Βsle → N6κΤ → δujE → ΞAζS → ΥktM → x8θi → ΩEβI → ΜΕZU → hUΚy → fGΩΑ → ΘKΥY → zYΖg → XIΧΙ → ΔaΔc → TQΞΝ → nivs
197,075×(max) 51 nodes96κι → δΨHE → ΞΕZS → lUΚu → f8θΑ → ΩKΥI → Ζyfa → VIΧΛ → Δezc → RKΥΟ → zmrg → J4μΨ → θΓbA → ΧQΞK → Βmre → N4μΤ → θujA → ΧAζK → ΥΑdM → xMΣi → vEβk → ΜAζU → ΥgxM → xGΩi → ΘEβY → ΜYΖU → hWΘy → bGΩΕ → ΘSΜY → jYΖw → XCδΙ → ΠaΔQ → pSΜq → j0πw → πCδ2 → ξΟP4 → κop8 → β0πG → πΙV2 → ξcΒ4 → κOΠ8 → βqnG → Κ2ξW → μcΒ6 → ζOΠC → ΣqnO → t2ξm → μ6κ6 → ζγDC → ΣΝRO → tktm
196,855×(max) 51 nodes70πλ → πγD2 → ξΝR4 → κkt8 → β8θG → ΩΙVI → ΖcΒa → VOΠΛ → rezo → L2ξΦ → μyf6 → ζIΧC → ΣΓbO → tQΞm → n6κs → δ4μE → θΝRA → ΧktK → Β8θe → ΩMΣI → Ζuja → VAζΛ → ΥezM → xKΥi → zEβg → ΜIΧU → Δgxc → RGΩΟ → ΘmrY → Z4μΗ → θWΘA → ΧaΔK → ΒSΜe → jMΣw → vCδk → ΠAζQ → ΥopM → x0πi → πEβ2 → ξΛT4 → κgx8 → βGΩG → ΚΗXW → dYΖΓ → XOΠΙ → raΔo → T2ξΝ → μiv6 → ζCδC → ΣΟPO → topm
196,271×(max) 51 nodesHCδα → ΠΗXQ → pYΖq → X0πΙ → πaΔ2 → ξSΜ4 → κiv8 → βCδG → ΠΙVQ → pcΒq → P0πΡ → πqn2 → ξ2ξ4 → μι76 → ζαFC → ΣΙVO → tcΒm → P6κΡ → δqnE → Ξ2ξS → μkt6 → ζ8θC → ΩΡNI → Ζsla → V6κΛ → δezE → ΞKΥS → zktg → J8θΨ → ΩΓbI → ΖQΞa → nUΚs → f4μΑ → θKΥA → ΧyfK → ΒIΧe → ΔMΣc → vQΞk → nAζs → Υ4μM → θwhA → ΧEβK → ΜΑdU → hMΣy → vGΩk → ΘAζY → ΥYΖM → xWΘi → bEβΕ → ΜSΜU → jgxw
195,015×(max) 51 nodesNGΩΤ → ΘujY → ZAζΗ → ΥWΘM → xaΔi → TEβΝ → ΜivU → hCδy → ΠGΩQ → ΘopY → Z0πΗ → πWΘ2 → ξaΔ4 → κSΜ8 → βivG → ΚCδW → ΠcΒQ → pOΠq → r0πo → π2ξ2 → ξλ54 → κεB8 → βΡNG → ΚslW → d6κΓ → δOΠE → ΞqnS → l2ξu → μ8θ6 → ζΨHC → ΣΕZO → tUΚm → f6κΑ → δKΥE → ΞyfS → lIΧu → Δ8θc → ΩQΞI → Ζmra → V4μΛ → θezA → ΧKΥK → Βyfe → NIΧΤ → Δujc → RAζΟ → ΥmrM → x4μi → θEβA → ΧΛTK → Βgxe
193,955×(max) 51 nodesF6κγ → δΛTE → ΞgxS → lGΩu → Θ8θY → ΩYΖI → ΖWΘa → bUΚΕ → fSΜΑ → jKΥw → zCδg → ΠIΧQ → Δopc → R0πΟ → πmr2 → ξ4μ4 → κη98 → βΦJG → ΚΑdW → dMΣΓ → vOΠk → rAζo → Υ2ξM → μwh6 → ζEβC → ΣΛTO → tgxm → H6κα → δΗXE → ΞYΖS → lWΘu → b8θΕ → ΩSΜI → Ζiva → VCδΛ → ΠezQ → pKΥq → z0πg → πIΧ2 → ξΓb4 → κQΞ8 → βmrG → Κ4μW → θcΒA → ΧOΠK → Βqne → N2ξΤ → μuj6 → ζAζC → ΥΡNM → xsli
52 cycles70,837,397×3 nodesΗWρΘZ → ΙXρΗX → ΘaρΔY
35,471,066×(max) 4 nodesΗXρΗZ → ΘWρΘY → ΙYρΖX → ΘZρΕY
66 cycles1,636,486,235×10 nodesdN7ιΣΓ → βuOΠkG → Κr9ηnW → Χd3νΒK → κΒNΡd8 → βtNΡlG → Κt7ιlW → βd7ιΒG → βΚNΡVG → ΚtdΑlW
183,145,569×(max) 28 nodesRK6κΦΟ → δΑmreE → ΞM4μΤS → θwktiA → ΧE8θγK → ΩΝΑdSI → ΖkMΣua → vV9ηΚk → ΧeAζΑK → ΥΒLΤdM → ywNΡih → tHDγΩm → ΞΗ6κYS → δlXΗtE → ΞZ7ιΖS → βlVΙtG → Κd7ιΒW → βdNΡΒG → ΚtNΡlW → td7ιΒm → βO6κΡG → δΚrmVE → Ξe4μΑS → θlLΤtA → Χx7ιhK → βΒFαdG → ΛΙNΡWV → tfbΓzm
91,111,327×2 nodesΧO4μΡK → θΒrmdA
2,431,411×10 nodesZK8θΦΗ → ΩΑWΘeI → ΖbLΤΔa → xVRΝΚi → leEβΑu → ΜM8θΤU → ΩwgxiI → ΖHDγΩa → ΞΗUΚYS → lfXΗzu
238,611×3 nodesΒC4μεe → θΡMΣOA → ΧvrmjK
140,932×2 nodesVLHΨΥΛ → Ζyezga
7+---Not showing digit sets 7+ due to verbosity.