Base 52: Maximum Iteration Sequences: Full Cycle

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
Full Cycle
12 max steps100
228 max steps20 → 1o → m3i7aFKVAfUL8hYHGZIXEbMT6jcDOR2nk5eBSN4lg9WJCdQP0po1m3
328 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 → PpQPpQ
416 max steps300D → D2md → kPP6 → dppC → dBdD → SPPO → 3ppm → m2m4 → kh76 → eZFC → SJVOC3leiRN8a3lGiJV8aBdGSJVO
526 max steps10003 → 30pon → pkp41 → okp42 → njp53 → mhp74 → lepA5 → kapE6 → jVpJ7 → iPpP8 → hIpW9 → gOpQA → fHpXB → eNpRC → dGpYD → cMpSE → bFpZF → aLpTG → ZEpaH → bIpWF → aIpWG → ZHpXH → YHpXI → YFpZIaGpYGZJpVHYFpZI
6192 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 → 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
742 max stepsQ00000o → oPpppP2 → nQPpPP3 → mO0poR4 → pkNpR51 → okMpS52 → njNpR63 → mhLpT84 → leLpTB5 → kaIpWF6 → jVHpXK7 → iSCpcN8 → hWEpaJ9 → gTGpYMA → fQBpdPB → eUDpbLC → dRFpZOD → cOApeRE → fQDpbPB → eSBpdNC → eSFpZNC → dPBpdQD → eQDpbPC → dRBpdODeQEpaPCdQApePDfRDpbOBeSCpcNCdSEpaNDcPCpcQEdOCpcRDdQDpbPDcQBpdPEePCpcQCdSCpcNDdQEpaPDcPApeQEfQCpcPBeTCpcMCdSFpZNDcOBpdREePDpbQCdRBpdOD
8450 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 → 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
956 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 → gWK8pgVJAhWNBpdSJ9gWK8pgVJA