Base 56: 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
211 max steps20 → 1s → q3m7eFOV6ngDSR0ts1q3
330 max steps100 → 0tt → st1 → rt2 → qt3 → pt4 → ot5 → nt6 → mt7 → lt8 → kt9 → jtA → itB → htC → gtD → ftE → etF → dtG → ctH → btI → atJ → ZtK → YtL → XtM → WtN → VtO → UtP → TtQ → StR → RtSRtS
421 max steps700S → S6mS → fttE → fDfF → SPTS → 3ttq → q2q4 → ol76 → idFC → WNVO → 96ml → gbHE → SJZS → Ftte → eEeG → QNVU → 83pm → mdF8 → eNVGO7lWe7lGeNVG
529 max stepsR0000 → QtttT → TPtTR → U1trQ → sQtS2 → rRtR3 → qPtT4 → pQtS5 → oOtU6 → nPtT7 → mNtV8 → lOtU9 → kMtWA → jNtVB → iLtXC → hMtWD → gKtYE → fLtXF → eJtZG → dKtYH → cItaI → bJtZJ → aHtbK → cGtcI → dJtZH → cJtZIbItaJbHtbJcHtbIcJtZI
6168 max steps1000GN → NG0sdX → sN9jW2 → qa8kJ4 → mcGcH8 → eMKYXG → OEAifW → YR7lSM → eC0shG → sVNVO2 → q86ml4 → mgcGD8 → eTLXQG → OC2qhW → oV7lO6 → ie6mFC → gWOUNE → S95nkS → iattIC → hb7lID → eUIaPG → OI4obW → kJ7laA → eaGcJG → OMGcXW → MB7liY → eXBhMG → WOAiVO → Y86mlM → gdBhGE → WSMWRO → A80slk → sdZJG2 → qNFdW4 → mO8kV8 → ec6mHG → gOKYVE → SE6mfS → gQttSE → fTDfQF → SQ2qTS → o2ttq6 → rn1r63 → qogC54 → mjTPA8 → eZ3pKG → mOEeV8 → eQ6mTG → gO2qVE → oS6mR6 → ig0sDC → sWSQN2 → q91rk4 → qmaI74 → mfHbE8 → eRJZSG → OG0sdW → sN7lW2 → qe8kF4 → mcOUH8 → eL5nYG → iOCgVC → WU6mPO → g84olE → kdRRGA → aMttWK → ZX3pML → mEAif8 → eYQSLG → OD1rgW → qT7lQ4 → me2qF8 → oeOUF6 → iP5nUC → iW4oNC → kW8kNA → ca8kJI → cKGcZI → MKEeZY → QFBheU → WP3pUO → m84ol8 → kecGFA → aPLXUK → GC4ohe → kVNVOA → a86mlK → gdFdGE → SOMWVS → A6ttmk → nj1rA7 → qgYKD4 → mTDfQ8 → eS2qRG → oO0sV6 → si6mB2 → qgWMD4 → mT9jQ8 → ea2qJG → oOGcV6 → iM6mXC → gWAiNE → YS8kRM → cC0shI → sVJZO2 → qG6md4 → mgMWD8 → eT9jQG → aO2qVK → oG6md6 → igMWDC → WT9jQO → a82qlK → odFdG6 → iOMWVC → WA6mjO → gZ7lKE → eSEeRG → QO0sVU → s73pm2 → qmeE74 → mfPTE8 → eR3pSG → mO0sV8 → se6mF2 → qgOUD4 → mT5nQ8 → ie2qFC → oWOUN6 → i95nkC → ibVNIC → WJ7laO → eH7lcG → eOKYVG → OE6mfW → gR7lSE → eS0sRG → sO0sV2 → sq6m32 → qnfD64 → mhRRC8 → eUttOG → dV9jOHaM6mXKgGAidEYSMWRMCA0sjisZVNK2qF7le4meOUF8eP5nUGiO4oVCkW6mNAga8kJEcSGcRIMK0sZYsFBhe2qWOUN4m95nk8ieaIFCWPHbUOK84olakdFdGAaOMWVKGA6mjegZNVKESF7leSeOttUGdV9jOH
743 max stepsI00000S → SHtttbS → cRQtSSI → bC0tshJ → tgNtVD1 → sgItaD2 → rfNtVE3 → qdHtbG4 → paLtXJ5 → oWEteN6 → naGtcJ7 → mXItaM8 → lUDtfP9 → kYFtdLA → jVHtbOB → iSCtgRC → hWEteND → gTGtcQE → fQBthTF → iSEteRC → hUCtgPD → hUGtcPD → gRCtgSE → hSEteRD → gTCtgQEhSFtdRDgSBthREiTEteQChUDtfPDgUFtdPEfRDtfSFgQDtfTEgSEteREfSCtgRFhRDtfSDgUDtfPEgSFtdREfRBthSFiSDtfRChVDtfODgUGtcPEfQCtgTFhREteSDgTCtgQE
8587 max steps70000DHK → KHD6mgca → gTLFdYQE → SOD2qgVS → oT6ttmQ6 → nnOIaV67 → hgI6mbDD → gUTIaQPE → SI52qobS → ojIttaA6 → njW8kNA7 → gcZ8kKHE → cSLEeYRI → QKD0sgZU → sTF3peQ2 → qmP2qU74 → omf4oE76 → kifQSEBA → aXR1rSMK → qGB0sid4 → smXMWM72 → qfB9jiE4 → maXQSMJ8 → eHB1ricG → qXOKYVM4 → mEB6mif8 → geXQSMFE → SPB1riUS → qX4ttoM4 → ppUGcP45 → lkM4oX99 → kcbAiIHA → aYLIaYLK → IGDCggdc → UTNJZWQQ → G942qpke → olbNVI86 → idJ7laGC → eWNGcWNG → OM98kkXW → cbB7liII → eXKIaZMG → OIFAiebW → YPJ7laUM → eHC4ohcG → kVOKYVOA → aE76mmfK → gfRFdSEE → SRO0sVSS → s70ttsm2 → trl5n821 → spicGB42 → qlXLXM84 → mdCAihG8 → eYVMWOLG → ODA6mjgW → gZT7lQKE → eSF2qeRG → oPO0sVU6 → si74omB2 → qkfWME94 → mbR9jSI8 → eaJ0saJG → sOHGccV2 → qML6mYX4 → mgDAigD8 → eYTSQQLG → OD31rqgW → qnT7lQ64 → mhe2qFC8 → oeVOUOF6 → iP75nmUC → ifW4oNEC → kWR8kSNA → ca90skJI → sbKGcZI2 → qMJEeaX4 → mQHAicT8 → eYL2qYLG → oODCggV6 → iUT6mQPC → gW52qoNE → ojS8kRA6 → icZ0sKHC → sWLEeYN2 → qQD8kgT4 → mcT2qQH8 → oeL2qYF6 → oiPCgUB6 → iXU4oPMC → kWB4oiNA → kaX8kMJA → caHAicJI → YLKGcZYM → MFDBhgeY → WTPBhUQO → W852qolO → ojd7lGA6 → ieZMWKFC → WPF9jeUO → aP84olUK → kdG4odGA → kaNMWWJA → aHA8kjcK → cZLFdYKI → OKFCgeZW → UPF7leUQ → eP53poUG → mjO4oVA8 → keZ6mKFA → gaPEeUJE → SQH4ocTS → kL2ttqYA → rjVBhOA3 → oZW6mNK6 → igF8keDC → cWTOUQNI → K962qnka → ohbFdIC6 → iVOIaVOC → WI76mmbO → gfJ7laEE → eSRGcSRG → OM10ssXW → srB7li22 → qpeWMF44 → mlP9jU88 → eda4oJGG → kONGcWVA → aM96mkXK → gbGAidIE → YSNIaWRM → IC90skhc → sbVJZOI2 → qJG6mda4 → mgNGcWD8 → eTM8kXQG → cOB2qiVI → oXK6mZM6 → igFAieDC → YWTOUQNM → C962qnki → ohbVNIC6 → iVJ7laOC → eWH6mcNG → gOL8kYVE → cSD6mgRI → gTK0sZQE → sSF2qeR2 → qoP0sU54 → smj4oA72 → qkfYKE94 → mbRDfSI8 → eSJ0saRG → sOH0scV2 → sqL6mY32 → qngCgD64 → mhUSQPC8 → eV51roOG → qjO6mVA4 → mgZ6mKD8 → geTEeQFE → SQP2qUTS → o52ttqo6 → rojtt953 → qoi4oB54 → mkjWMA98 → ebZ9jKIG → aOJEeaVK → QHG6mdcU → gNL3pYWE → mSD8kgR8 → ecT0sQHG → sOL2qYV2 → qoD6mg54 → mjgSQDA8 → eZT1rQKG → qOF2qeV4 → omP6mU76 → igf4oEDC → kWTQSQNA → a931rqkK → qnbFdI64 → mhOIaVC8 → eVI6mbOG → gOJ6maVE → gSH6mcRE → gSL0sYRE → sSD0sgR2 → sqT0sQ32 → sqn2q632 → qongC654 → mjhTPCA8 → eZV3pOKG → mOF6meV8 → geP6mUFE → gSP4oURE → kS50soRA → sja0sJA2 → sqZGcK32 → qnMEeX64 → mhQAiTC8 → eYV2qOLG → oOD6mgV6 → igT6mQDC → gWT2qQNE → oS92qkR6 → oib0sIB6 → siXIaMB2 → qXIAibM4 → mYJAiaL8 → eYHCgcLG → UOLCgYVQ → UD73pmgQ → mfT3pQE8 → meR2qSF8 → oeP0sUF6 → siP4oUB2 → qkX4oM94 → mkbAiI98 → ebYIaLIG → OJICgbaW → UJH7lcaQ → eLH3pcYG → mOLCgYV8 → eUD6mgPG → gTO4oVQE → kS72qmRA → ofa0sJE6 → siRGcSB2 → qXM0sXM4 → smBAii72 → qfYWMLE4 → mRD9jgS8 → eaT0sQJG → sOH2qcV2 → qoL6mY54 → mjgCgDA8 → eZUSQPKG → OF51roeW → qjP7lUA4 → meZ4oKF8 → kePEeUFA → aQP4oUTK → kG52qodA → ojaMWJA6 → iZH9jcKC → aWLEeYNK → QGD8kgdU → cTN3pWQI → mK92qkZ8 → oebEeIF6 → iQPIaUTC → WI52qobO → ojJ7laA6 → ieZGcKFC → WPMEeXUO → QB84oliU → kdX3pMGA → maNAiWJ8 → eYH8kcLG → cOLCgYVI → UKD6mgZQ → gTF3peQE → mSP2qUR8 → oe50soF6 → sjiOUBA2 → qZX5nMK4 → miFAieB8 → eYXOUMLG → ODB5nigW → iXT7lQMC → eWB2qiNG → oXO8kVM6 → icB6miHC → gXWKYNME → SEB8kifS → cXQttSMI → bXC4ohMJ → kVIAibOA → aYJ6maLK → gHGCgdcE → USNKYWRQ → E940spkg → slbRRI82 → qdIttaG4 → pdY2qLG5 → okNCgW96 → ibU8kPIC → cWJ4oaNI → kKH8kcZA → caLEeYJI → QKHCgcZU → ULF3peYQ → mPD3pgU8 → meT4oQF8 → keP2qUFA → oaP4oUJ6 → kiH4ocBA → kaXKYMJA → aHEAifcK → YRLFdYSM → ODC0shgW → sVT7lQO2 → qe72qmF4 → omfOUE76 → ifR5nSEC → iWR0sSNC → sW90skN2 → sqb8kI32 → qncIaH64 → mhLHbYC8 → eVKCgZOG → UOF6meVQ → gP73pmUE → mfS4oRE8 → keR0sSFA → saP0sUJ2 → sqH4oc32 → qnkKY964 → mhbDfIC8 → eVSIaROG → OI70smbW → sfJ7laE2 → qeRGcSF4 → mPM0sXU8 → seB4oiF2 → qkXOUM94 → mbB5niI8 → ieXIaMFC → WPIAibUO → YJ84olaM → kdHBhcGA → aWNKYWNK → GE98kkfe → cbRNVSII → KJ80slaa → sdHFdcG2 → qONKYWV4 → mE96mkf8 → gebQSIFE → SPJ1raUS → qH4ttoc4 → ppZBhK45 → lkWEeN99 → cbQ8kTII → cKJ2qaZI → oKHEecZ6 → iQLEeYTC → WQD2qgTO → oT82qlQ6 → oid2qGB6 → oiXMWMB6 → iXB9jiMC → aXWAiNMK → YGB8kidM → cXNBhWMI → WKB8kiZO → cXF7leMI → ePKAiZUG → YOF4oeVM → kPC6mhUA → gaV4oOJE → kSH6mcRA → gaL0sYJE → sSHCgcR2 → qUL0sYP4 → smD4og72 → qkfSQE94 → mbR1rSI8 → qeJ0saF4 → smPGcU72 → qfM4oXE4 → mkRAiS98 → ebY0sLIG → sOJCgaV2 → qUH6mcP4 → mgL4oYD8 → keTCgQFA → aUP2qUPK → oG54ood6 → kjiMWBAA → aZX9jMKK → aGFAiedK → YPNFdWUM → OC94okhW → kbV7lOIA → eaJ6maJG → gOHGccVE → SML6mYXS → gDAttigE → jgTttPDB → igKCgZDC → WUTEeQPO → Q852qolU → ojd3pGA6 → miZMWKB8 → eXF9jeMG → aPOAiVUK → YG74omdM → kfNBhWEA → aWR8kSNK → cG90skdI → sbNJZWI2 → qJG8kda4 → mcNGcWH8 → eML8kYXG → cODAigVI → YTK6mZQM → gFC2qheE → oVSOURO6 → i760snmC → shfVNEC2 → qVR7lSO4 → me70smF8 → sfeOUFE2 → qRP5nUS4 → mi50soB8 → sjeWMFA2 → qZP9jUK4 → maF4oeJ8 → kePGcUFA → aPM4oXUK → kGB4oidA → kaXMWMJA → aHB9jicK → aXLFdYMK → OGDAigdW → YTN7lWQM → eC92qkhG → obVNVOI6 → iJ86mlaC → gdWGcNGE → SNM8kXWS → cB8ttkiI → liS5nRB9 → icX0sMHC → sWLAiYN2 → qYD8kgL4 → mcTCgQH8 → eUL2qYPG → oOD4ogV6 → kiT6mQBA → gaX2qMJE → oSHAicR6 → iYL0sYLC → sWDCggN2 → qUT8kQP4 → mc52qoH8 → ojeKYFA6 → iZPDfUKC → WSF4oeRO → kP80slUA → sda4oJG2 → qkNGcW94 → mbM8kXI8 → ecJAiaHG → YOLGcYVM → MDC6mhgY → gVTBhQOE → WS72qmRO → of80slE6 → sidQSGB2 → qXN1rWM4 → qmB8ki74 → mfcWMHE8 → eRL9jYSG → aOD0sgVK → sTG6mdQ2 → qgN2qWD4 → omT8kQ76 → ifc2qHEC → oWRKYSN6 → 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