Base 57: 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
217 max steps10 → 0u → t1 → r3n7fFPV5pjBXN9lbJHdLZDhTR1tr3
331 max steps100 → 0uu → tu1 → su2 → ru3 → qu4 → pu5 → ou6 → nu7 → mu8 → lu9 → kuA → juB → iuC → huD → guE → fuF → euG → duH → cuI → buJ → auK → ZuL → YuM → XuN → WuO → VuP → UuQ → TuR → SuSRuTSuS
413 max stepsT000 → SuuS → SRST → 1uut → t0t2tq32rm74neF8fOVGP6nWh6nEhSRET0tSt0t2
528 max steps10000 → 0uuuu → tuuu1 → t0ut2 → uqu31 → tqu32 → spu43 → rnu64 → qku95 → pguD6 → obuI7 → nVuO8 → mOuV9 → lNuWA → kNuWB → jMuXC → iMuXD → hLuYE → gLuYF → fKuZG → eKuZH → dJuaI → cJuaJ → bIubK → cGudJ → eJuaH → dKuZI → cIubJcIubJ
6159 max stepsH000SY → YSGdSN → NAuujY → kXAjNB → aY9kML → bFBifK → XQGdUO → N93qlY → ncAjI8 → fZJaLG → PHDgdW → TM6nYS → hC0tiE → tWSRO2 → r80tm4 → tndG72 → rgMXE4 → nSAjS8 → fYuuLG → eZ6nLH → hNDgXE → US9kSR → b2uurK → saFeK3 → pPFeV6 → jP5oVC → jX5oNC → jX9kNC → bX9kNK → bH9kdK → bMGdYK → NHBidY → XMAjYO → ZC8liM → dWChOI → VL7mZQ → fE4pgG → lSOVSA → b6uunK → oaBiK7 → hXFeNE → TP9kVS → b60toK → tiGdC2 → rWMXO4 → nB7mj8 → geXMGF → ROAjWU → Z82rmM → peChG6 → jVNWPC → X95olO → jc8lIC → dXJaNI → LH9kda → bMEfYK → RHBidU → XM2rYO → pC8li6 → jdVOHC → XM6nYO → hC8liE → dWSROI → L80tma → teEfG2 → rRNWT4 → n91sl8 → rfbIF4 → nQIbU8 → fJ3qbG → nPHcV8 → fL5oZG → jPDgVC → XT5oRO → j91slC → rcWNI4 → nK8la8 → fdFeHG → QOLYWV → D84pmi → leUPGA → bO4pWK → lH7mdA → fbLYJG → PIChcW → VK6naQ → hG4peE → lTNWRA → b91slK → rcGdI4 → nNJaX8 → fH9kdG → bPLYVK → HD5ohe → jUMXQC → XB3qjO → nY8lM8 → fdBiHG → XPLYVO → D95oli → jcUPIC → XK4paO → lG8leA → dbNWJI → LI8lca → dKEfaI → RLFeZU → PE2rgW → pS6nS6 → jguuDC → ih2rDD → pVTQP6 → j62roC → piWNC6 → jW8lOC → dX7mNI → fL9kZG → bPDgVK → TH5odS → jM0tYC → tXBiN2 → rX9kN4 → nb9kJ8 → fbHcJG → PLHcZW → LE6nga → hSEfSE → TQuuTS → URuuSR → TT1sRS → r20ts4 → tqm742 → rmeF84 → neOVG8 → fO6nWG → hP7mVE → fT5oRG → jP1sVC → rX5oN4 → nj9kB8 → fbXMJG → PIAjcW → ZK6naM → hGCheE → VTNWRQ → 951spmrkcHA4naKZK8fGEfeGRPNWVU962rompicHC6jWKZOCXF7mfOfQ8lUGdP3qVInL5oZ8jfDgFCXTPURO951spm
738 max steps1000016 → 610uttp → usmu721 → tsku922 → sriuB33 → rpfuE54 → qmauJ85 → piSuRC6 → odGudH7 → nYLuYM8 → mSBuiS9 → lbFueJA → kWKuZOB → jQAujUC → kXIubNB → jSDugSC → iWDugOD → hVHucPE → gQCuhUF → iSFueSD → hTBuiRE → jUFueQC → iUDugQD → hVFuePE → gSEufSF → gRCuhTF → iSEufSD → hUCuhQE → iTGudRD → hSBuiSE → jUEufQC → iVEufPD → hUFueQE → gSDugSF → hRDugTE → hTEufRE → gTDugRFhREufTEgTDugRF
8315 max stepsC0000HSY → YSHBidSN → XMAuujYO → kYL0tZMB → tZEBigL2 → rXSDgSN4 → nT9uukR8 → mlMGdY99 → dcNBiXII → XLK9kaZO → bGE8lgeK → dSOGdWSI → NL7uumZY → nZP0tVL8 → tfE5ogF2 → rjSPUSB4 → nY4uupM8 → qmTEfR85 → leR1sTGA → rbO1sWJ4 → rnI7mc74 → ngfJaFE8 → fSQGdUSG → PN3uuqXW → rXR0tTN4 → tnA1sk72 → sqgZKE43 → pmSEfS86 → jeQuuTGC → ieJAjbGD → ZVOHcWPM → LD85omha → jeUEfQGC → XRO3qWTO → n981sml8 → rfebIGF4 → nQOIbWU8 → fJ83qmbG → nePHcVG8 → fOL5oZWG → jPE7mgVC → fXS5oSNG → jP9uukVC → liLDgZCA → bWTDgROK → TH81smdS → reM0tYG4 → tnOBiW72 → rgX7mNE4 → nfS9kSF8 → fbPuuUJG → ebG6neJH → hONHcXWE → TLA7mkZS → faE0tgKG → tSPFeVS2 → rP5uuoV4 → qpSIbS55 → lkIuubAA → kkT8lRAB → daZ1sLKI → rLGDgeZ4 → nTODgWR8 → fT81smRG → reP1sVG4 → rnO5oW74 → njg7mEB8 → geYRSMGF → ROC0tiWU → tW82rmO2 → rpe7mG54 → nkfNWFA8 → faQ8lUKG → dPG3qeVI → nOL5oZW8 → jfE7mgFC → fXSPUSNG → PA4uupkW → qkQDgUA5 → laT3qRKA → nbG1seJ8 → rfOHcWF4 → nQL7mZU8 → geE3qgGF → nSRNWTS8 → f91uuslG → tlc5oI92 → rjcJaIB4 → nYKGdaM8 → fNGBieXG → XPO9kWVO → b985omlK → jecGdIGC → XONJaXWO → HA97mlke → fcaMXKIG → PKGAjeaW → ZOG6neWM → hOD7mhWE → fUT7mRQG → fP41sqVG → rmP5oV84 → nje5oGB8 → jfYNWMFC → XQC8liUO → dW93qlOI → ncL7mZI8 → geKDgaGF → TROFeWTS → P820tsmW → tqe6nG42 → rmhNWD84 → neU8lQG8 → fdO3qWHG → nPM7mYV8 → geC5oiGF → jWRNWTOC → X981smlO → rec8lIG4 → ndOJaWH8 → fMH7mdYG → fPMBiYVG → XPC5oiVO → jW95olOC → jcX7mNIC → fXK9kaNG → bPG9keVK → bOH5odWK → jMH7mdYC → fXMBiYNG → XPC9kiVO → bW95olOK → jcH7mdIC → fXMJaYNG → PHC9kidW → bWM6nYOK → hHC7midE → fWTLYROG → PD81smhW → reU6nQG4 → nhO3qWD8 → nfU7mQF8 → geQ3qUGF → nRO3qWT8 → nf81smF8 → rfePUGF4 → nQO4pWU8 → lf83qmFA → nebPUJG8 → fOI4pcWG → lPK7maVA → fbG5oeJG → jPOHcWVC → XL85omZO → jeE8lgGC → dXSNWSNI → LA8uulka → mkQ9kUA9 → dba3qKJI → nLIFecZ8 → fPKDgaVG → TPG5oeVS → jO60toWC → tiX7mNC2 → rfW9kOF4 → nbQ7mUJ8 → geI3qcGF → nROJaWT8 → fH81smdG → rePLYVG4 → nOD5ohW8 → jfU7mQFC → fXQ3qUNG → nPA3qkV8 → nfa5oKF8 → jfQFeUFC → XQP3qVUO → n963qol8 → nifbIFC8 → fWQIbUOG → PJ83qmbW → neI6ncG8 → hfOJaWFE → TQH7mdUS → fM40tqYG → tmPBiV82 → reX5oNG4 → njO9kWB8 → fbY7mMJG → fPIBicVG → XPK5oaVO → jG95oleC → jcXNWNIC → XKA8lkaO → daG8leKI → dOLFeZWI → PLE7mgZW → fSE6ngSG → hSOuuVSE → gWF2rfOF → pRQ7mUT6 → jf41sqFC → rmXPUN84 → neA4pkG8 → lfaNWKFA → bQG8leUK → dOH3qdWI → nML7mZY8 → geEBigGF → XSRNWTSO → A81uusml → tmi0tC82 → treVOG32 → roO6nW64 → nih7mDC8 → geWTQOGF → RO82rmWU → pe82rmG6 → pjeNWGB6 → jYO8lWMC → dXC7miNI → fWL9kZOG → bPE7mgVK → fSH5odSG → jPLuuYVC → iZK2raLD → pVGDgeP6 → jTO5oWRC → jX81smNC → reX9kNG4 → nbO9kWJ8 → fbI7mcJG → fPKHcaVG → PLG5oeZWjOE6ngWChXS7mSNEfT9uukRGleJBibGAbXOHcWNKLHA7mkdafaMEfYKGRPGBieVUXO62roWOpi97mlC6jfcVOIFCXQK6naUOhG93qleEncTNWRI8fK91slaGrcPFeVI4nPK5oaV8jfG5oeFCjXQNWUNCXA93qlkOnca8lKI8fdKFeaHGQOMFeYWVPC84pmiWleW6nOGAhbO7mWJEfTI7mcRGfPK1saVGrPG5oeV4njO5oWB8jfY7mMFCfXQBiUNGXPA3qkVOna95olK8jfcFeIFCXQPJaVUOH963qolenicMXIC8fWKAjaOGZPG7meVMfOD5ohWGjUP7mVQCfX63qoNGniP9kVC8fbW5oOJGjPI7mcVCfXK5oaNGjPG9keVCbXO5oWNKjHA7mkdCfaXLYNKGPGD9kheWbUO6nWQKhH83qmdEneTLYRG8fOD1shWGrUP7mVQ4nf63qoF8nifPUFC8fWQ4pUOGlP83qmVAneb5oJG8jfOHcWFCXQL7mZUOfE93qlgGncSOVSI8fK6uunaGoeT4pRG7lhO1sWDArbU7mQJ4nfI3qcF8nfQJaUF8fQH3qdUGnPM3qYV8nfC5oiF8jfWPUOFCXQ84pmUOle93qlGAncbNWJI8fKI8lcaGdPKFeaVIPLG5oeZW