Base 56: 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 → 1s → q3
329 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 → RtS
418 max steps700S → S6mS → fttE → fDfF → SPTS → 3ttq → q2q4 → ol76 → idFC → WNVO → 96ml → gbHE → SJZS → Ftte → eEeG → QNVU → 83pm → mdF8 → eNVG
525 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 → cJtZI
6142 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 → dV9jOH
724 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 → gTCtgQE
8473 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 → iE90skfC