Base 52: Maximum Iteration Sequences: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ

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 Max Steps Max Step Example
Cycle Start
11 max steps10
22 max steps20 → 1o → m3
327 max steps100 → 0pp → op1 → np2 → mp3 → lp4 → kp5 → jp6 → ip7 → hp8 → gp9 → fpA → epB → dpC → cpD → bpE → apF → ZpG → YpH → XpI → WpJ → VpK → UpL → TpM → SpN → RpO → QpP → PpQ
410 max steps300D → D2md → kPP6 → dppC → dBdD → SPPO → 3ppm → m2m4 → kh76 → eZFC → SJVO
523 max steps10003 → 30pon → pkp41 → okp42 → njp53 → mhp74 → lepA5 → kapE6 → jVpJ7 → iPpP8 → hIpW9 → gOpQA → fHpXB → eNpRC → dGpYD → cMpSE → bFpZF → aLpTG → ZEpaH → bIpWF → aIpWG → ZHpXH → YHpXI → YFpZI
684 max steps90000J → J8ppgX → hW8gJ9 → ZXCcIH → QIEaXQ → MEppaU → bT5jMF → eM6iTC → cS6iNE → cO4kRE → gO2mRA → kW2mJ6 → keCcB6 → eTPPMC → S6ppiO → jRFZO7 → cK2mVE → kOAeR6 → eU2mLC → kS8gN6 → eY4kHC → gSGYNA → WI4kXK → gFBdaA → WSKUNK → CA4kfe → gVRNKA → WB3leK → iTBdM8 → aS6iNG → cK4kVE → gOAeRA → WU2mLK → kC8gd6 → eYQOHC → SH1nYO → mH3lY4 → jhGY87 → cZHXGE → OJFZWS → KD3lcW → iPBdQ8 → aS0oNG → oK4kV2 → mgAe94 → iXTLI8 → aF7haG → aLJVUG → KC8gdW → YRBdOI → SG2mZO → kJ3lW6 → ieCcB8 → aTPPMG → K6ppiW → jVBdK7 → cSAeNE → UO4kRM → g82mhA → kZVJG6 → eJBdWC → TRCcON → Q62mjQ → kcppC6 → jd7hC7 → caQOFE → OL1nUS → m93lg4 → jhWI87 → cZDbGE → PNIWSR → E51nkc → mfNRA4 → iV3lK8 → iaAeF8 → aUKULG → KA8gfW → YVBdKI → SGAeZO → UJ3lWM → iD7hc8 → bZOQGF → MJ1nWU → mD7hc4 → iaOQF8
723 max stepsQ00000o → oPpppP2 → nQPpPP3 → mO0poR4 → pkNpR51 → okMpS52 → njNpR63 → mhLpT84 → leLpTB5 → kaIpWF6 → jVHpXK7 → iSCpcN8 → hWEpaJ9 → gTGpYMA → fQBpdPB → eUDpbLC → dRFpZOD → cOApeRE → fQDpbPB → eSBpdNC → eSFpZNC → dPBpdQD → eQDpbPC → dRBpdOD
8337 max steps30000Noo → ooN2mS12 → nmk4k533 → kjgeA966 → edXTLICC → SRF7haOO → aL42mlUG → khK8gV86 → eZYAeHGC → USJGYWNM → ID84khcY → gZPFZQGA → WKJ0oWVK → oDCAedc2 → mUROQOL4 → i931nmg8 → mjaWIF64 → idLDbUC8 → aRO8gROG → YK32mmVI → kjGAeZ66 → edUIWLCC → SRE8gbOO → YN42mlSI → khG4kZ86 → geZIWGBA → WTJDbWMK → ODC6idcS → cRP3lQOE → iO30omR8 → oja2mF62 → mkdKUC54 → ifR9fOA8 → aWV2mKJG → kKDAecV6 → eUPAeQLC → US90ogNM → oX84khI2 → mgZEaG94 → iXMIWTI8 → aFE6ibaG → cNLJVUSE → OC94kgdS → gXR3lOIA → iWF2maJ8 → kaLCcUF6 → eQL8gUPC → YS90ogNI → oXG4kZI2 → mgJEaW94 → iXMCcTI8 → aQF6iaPG → cLK0oVUE → oOB8geR2 → mYT2mMH4 → kiH6iY76 → ecbGYEDC → SPNHXSQO → G540olka → ohfJVA82 → mZVBdKG4 → iSJAeWN8 → aUD4kcLG → gPK8gVQA → YWB0oeJI → oTGCcZM2 → mQJ6iWP4 → icD0ocD8 → oaPOQQF2 → mL20onU4 → oli8g742 → mhbXHE84 → iZNFZSG8 → aKJ4kWVG → gKDAecVA → WUPAeQLK → UC90ogdM → oXR7hOI2 → maF2maF4 → kiLKUU76 → ebA8gfEC → YVSMSNKI → GB64kjea → gdTJVMCA → WRC6idOK → cRC2mdOE → kRO2mRO6 → ke32mmB6 → kjeSMB66 → edT5jMCC → eSR6iONC → cS52mkNE → kfO4kRA6 → geV2mKBA → kWTAeMJ6 → eUD6icLC → cSP8gQNE → YO50okRI → ofG2mZA2 → mkVIWK54 → ifEAebA8 → aVUMSLKG → KB95jgeW → eXTBdMIC → TRF6iaON → cL62mjUE → kdO8gRC6 → eYR2mOHC → kSH2mYN6 → keH4kYB6 → geTGYMBA → WTI6iXMK → cFC6idaE → cROKUROE → OA32mmfS → kjV3lK66 → iedAeCB8 → aUTQOMLG → K971nigW → mbXBdIE4 → iSNEaSN8 → aM54kkTG → gfK6iVAA → cWVAeKJE → UODAecRM → UP82mhQM → kZ80ohG6 → oeZIWGB2 → mTJDbWM4 → iOD6icR8 → caP2mQFE → kOL0oUR6 → oe92mgB2 → mkXSMI54 → ifF5jaA8 → eaVKUKFC → SLB9feUO → WT93lgMK → iXC6idI8 → caREaOFE → OML2mUTS → k973lig6 → iebWIEB8 → aTNDbSMG → OK74kiVS → gbB3leEA → iWTMSMJ8 → aD75jicG → ebPJVQEC → SNC0odSO → oR53lkO2 → mif2mA74 → kibUKE76 → ebN9fSEC → WSN4kSNK → gC54kkdA → gfWQOJAA → WVD1ncKK → mPCAedQ4 → iUR0oOL8 → oa92mgF2 → mkXKUI54 → ifF9faA8 → aWVKUKJG → KDB9fecW → WTPBdQMK → SC70oidO → obR3lOE2 → miN2mS74 → kib4kE76 → gebMSEBA → WTN5jSMK → eC74kidC → gbSQONEA → WN51nkSK → mfC4kdA4 → igVQOK98 → aXB1neIG → mTKEaVM4 → iMB6ieT8 → caT6iMFE → cOL6iURE → cO92mgRE → kXO2mRI6 → keF2maB6 → keTKUMB6 → eTA6ifMC → cVS6iNKE → cOB4keRE → gTO2mRMA → kW72miJ6 → kebCcEB6 → eTQMSPMC → S760ojiO → odb3lEC2 → miRMSO74 → ib62mjE8 → kdaMSFC6 → eRL5jUOC → eS92mgNC → kXS4kNI6 → geF4kaBA → gWTKUMJA → WDA6ifcK → cVPBdQKE → SOB0oeRO → oT42mlM2 → mkh6i854 → ifcYGDA8 → aVPHXQKG → KGB0oeZW → oTJBdWM2 → mSD6icN4 → icP4kQD8 → gaP0oQFA → oWL0oUJ2 → omD8gc32 → mjYOQH64 → idH1nYC8 → maRGYOF4 → iLI2mXU8 → kaF8gaF6 → eYLKUUHC → SHA8gfYO → YVH3lYKI → iHGAeZY8 → aUJGYWLG → KID8gcXW → YPFBdaQI → SLG0oZUO → oJ93lgW2 → miXCcI74 → ibQEaPE8 → aNM0oTSG → oK74kiV2 → mgbAeE94 → iXUMSLI8 → aF95jgaG → eXLJVUIC → SFC8gdaO → YRL3lUOI → iG92mgZ8 → kaXIWIF6 → eLFDbaUC → SOL8gURO → Y942mlgI → khXFZI86 → eZKEaVGC → SMJAeWTO → UD73licM → ibP7hQE8 → bZN0oSGF → oMJ4kWT2 → mgD6ic94 → icXOQID8 → aPF1naQG → mLK0oVU4 → oiB8ge72 → mbYSMHE4 → iNH5jYS8 → eaH4kYFC → gSLGYUNA → WI94kgXK → gXFBdaIA → WSLEaUNK → MC94kgdU → gXR7hOIA → aWF2maJG → kLKCcVU6 → eQB8gePC → YTS0oNMI → oG74kiZ2 → mgbIWE94 → iXNDbSI8 → aOF4kaRG → gLK2mVUA → kWB8geJ6 → eYTCcMHC → SQH6iYPO → cH40olYE → ohOGYR82 → mZI2mXG4 → kiJEaW76 → ebMCcTEC → SQN6iSPO → c540olkE → ohfNRA82 → mZV3lKG4 → jhJAeW87 → cZUCcLGE → QOJ8gWRQ → YD2ppmcI → ncU3lLD3 → kiP8gQ76 → ebY0oHEC → oSNGYSN2 → mI54kkX4 → igfEaA98 → aXVLTKIG → KFB7heaW → aTLBdUMG → SK96igVO → cXB3leIE → iTOEaRM8 → aM72miTG → kbK6iVE6 → ecNAeSDC → USP4kQNM → g850okhA → ofZVJGA2 → mVJBdWK4 → iSDAecN8 → aUP4kQLG → gK90ogVA → oXWAeJI2 → mUFCcaL4 → iQL8gUP8 → aY90ogHG → oXKGYVI2 → mIFAeaX4 → iULEaUL8 → aM98ggTG → YXK6iVII → cGFAeaZE → UOLIWURM → E982mhgc → kZXNRIG6 → eJF3laWC → iSLCcUN8 → aQ94kgPG → gXK0oVIA → oWFAeaJ2 → mULCcUL4 → iQ98ggP8 → aYX0oIHG → oKHEaYV2 → mMHAeYT4 → iUH6iYL8
954 max stepsP00000000 → OpppppppR → RNpppppRP → SQONpRRPO → S431pnmlO → okiMpS752 → njdLpTC63 → mhXHpXI84 → leQEpaPB5 → kaQApePF6 → jaPApeQF7 → iZPApeQG8 → hYO9pfRH9 → gYO9pfRHA → gWO9pfRJA → gWM7phTJA → iXN9pfSI8 → hZN9pfSG9 → gYPBpdQHA → fVM8pgTKB → hVL8pgUK9 → hYM9pfTH9 → gYOBpdRHA → fVM9pfTKB → gUL8pgULA → hWL8pgUJ9 → hYNApeSH9 → gXNApeSIA → fWM9pfTJB → gUM9pfTLA → gWK7phVJA → iXNBpdSI8 → hXL9pfUI9 → gYNBpdSHA → fVMApeTKB → fUK8pgVLB → hVL9pfUK9 → gYL9pfUHA → gWOCpcRJA → fUJ7phWLB → iWMApeTJ8 → hYL9pfUH9 → gYOCpcRHA → fUL9pfULB → gUK8pgVLA → hWM9pfTJ9 → gYM9pfTHA → gWOBpdRJA → fVK7phVKB → iWLApeUJ8 → hYLApeUH9 → gXNCpcSIA → fUK9pfVLB → gUL9pfULA → gWK8pgVJA