Base 49: 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
213 max steps10 → 0m → l1 → j3f7XFHVDZLR5hbBPN1lj3
327 max steps100 → 0mm → lm1 → km2 → jm3 → im4 → hm5 → gm6 → fm7 → em8 → dm9 → cmA → bmB → amC → ZmD → YmE → XmF → WmG → VmH → UmI → TmJ → SmK → RmL → QmM → PmN → OmONmPOmO
425 max stepsP000 → OmmO → ONOP → 1mml → l0l2li32je74fWF8XGVGHEXWJEXUJAbURAbMR4hMd4hAdSJAT8dKV8dIVCZINCZQN2jQh2j6haB6bONCP0lOl0l2
526 max steps10000 → 0mmmm → lmmm1 → l0ml2 → mim31 → lim32 → khm43 → jfm64 → icm95 → hYmD6 → gTmI7 → fNmO8 → eHmU9 → dMmPA → cGmVB → bLmQC → aFmWD → ZKmRE → YEmXF → YImTF → XFmWG → XGmVG → WGmVH → WEmXHYFmWFXImTGWEmXH
6126 max stepsD000gg → ggCZ67 → aZMPDD → NM2jQQ → h42ji6 → heaB86 → bWONGC → PG0lWO → lG0lW2 → ljFW32 → jgGV64 → faEXC8 → XOITOG → HAmmbW → cV4hHB → dRDYLA → TL5gRK → b95gdC → bUONIC → PC0laO → lO0lO2 → limm32 → kj2j33 → igf665 → daYDCA → TOKROK → 96mmfe → gd0l97 → lZTID2 → jMAbQ4 → fR3iL8 → fX5gF8 → bXHUFC → PICZUO → NC0laQ → lO2jO2 → jgmm54 → ih2j55 → hdbA96 → bUQLIC → PC4haO → dO0lOA → lSmmJ2 → kTITJ3 → hB9cb6 → bTPMJC → PA2jcO → hS0lK6 → lb7eB2 → jXPMF4 → fI2jU8 → hXBaF6 → bPHUNC → PD1kZO → jM0lQ4 → lf3i72 → jfXE74fYITE8XKAbSGRH7eVMXE4hYGdKGVSATF7eXKXI8dUGVHBaVIPECZYONK0lSQl82je2jhVG54fcEXA8XSITKGHB7ebWXQEXMGJH3iVUfEAbY8XRJSLGH95gdWbUEXICPJBaTOPA0lcOlS0lK2lj7e32jgWF64faGVC8XOEXOGJGmmVUWT0lJHlF9cX2jTHUJ4fD9cZ8XTLQJGHA4hcWdSEXKATJ7eTKXA8dcGVSGVKIFD7eZYXMITQGHB3ibWfQEXM8XJ3iTGfH9cV8XTDYJGLH9cVSTE6fYKZK8dSEVL7eRIXD5gZGbMGVQCPF3iXOfI0lU8lXBaF2jPHUN4fD1kZ8jXLQF4fI4hU8dXBaFATPHUNKD91kdajUMPI4fC2ja8hXNOF6bI0lUClPBaN2jP1kN4jf1k74jfXE74
734 max stepsD00000b → bCmmmZC → aaCmZCD → aOMmPOD → ZE0mlYE → mXKmRF1 → lXCmZF2 → kZJmSD3 → jXFmWF4 → iUHmUI5 → hRBmaL6 → gWEmXG7 → fSGmVK8 → ePAmbN9 → dUDmYIA → cQFmWMB → bN9mcPC → dQDmYMA → cQBmaMB → bRDmYLC → aOCmZOD → aNAmbPD → cOCmZOB → bQAmbMC → cPEmXNB → bO9mcOC → dQCmZMA → cRCmZLB → bQDmYMC → aOBmaOD → bNBmaPC → bPCmZNC → aPBmaNDbNCmZPCaPBmaND
8149 max stepsE0000FOW → WOFDYXOH → LIEmmXUS → YUC1kaIF → jOJBaTO4 → fP9mmcN8 → edICZU99 → VUNBaPII → PDC1kaZO → jOM0lQO4 → lf3mmi72 → kje2j833 → iggVG665 → daaEXCCA → TOOITOOK → B8mmmmdc → ebA8dcB9 → WUSPMKIH → FC82jeaY → hWOITOG6 → bGAmmbWC → caL4hRCB → dRO5gOLA → bT5mmgJC → haN7ePC6 → bXO1kOFC → jPHmmUN4 → iVM4hQH5 → ecE3iYA9 → fVSJSKH8 → XE97edYG → XUKGVSIG → HFC7eaXW → XOIEXUOG → JHBmmaVU → bVH0lVHC → lPEDYYN2 → jLK1kSR4 → jf85ge74 → fbYVGEB8 → XQKEXSMG → JH83ieVU → fWEAbYG8 → XRKFWSLG → IG85geWV → bWGCZWGC → PNGFWWPO → HG20lkWW → liGEXW42 → jeJFWT84 → fWH9cVG8 → XTGDYWJG → LHG9cWVS → TGE6fYWK → ZKG8dWSE → VLG7eWRI → XGD5gZWG → bMHFWVQC → PHE3iYVO → fKE0lYS8 → lXK7eSF2 → jXI7eUF4 → fXIBaUF8 → XPIBaUNG → PHC1kaVO → jOE0lYO4 → lfJmmS72 → kfSCZK73 → hYN7ePE6 → bXK1kSFC → jPI7eUN4 → fXC1kaF8 → jXOHUOF4 → fICmmZU8 → eaN4hPC9 → dVO1kOHA → jTDmmYJ4 → iZQ4hMD5 → ecM3iQA9 → fVS3iKH8 → fXE7eYF8 → YWKHUSGF → JGD7eZWU → XMGAbWQG → RHG3iWVM → fGE4hYW8 → dXKFWSFA → TIH7eVUK → XEC8daYG → VOKGVSOI → FD7mmeZY → fZP0lND8 → lXM1kQF2 → kiI3iU43 → hfeBa876 → bYWONGEC → PKG0lWSO → lG80leW2 → ljWFWG32 → jgHFWV64 → faHDYVC8 → XOLDYROG → LH5mmgVS → hVL2jRH6 → hbE5gYB6 → caQJSMCB → RO93idOM → fU4mmhI8 → iePAbN85 → dWR1kLGA → jTG5gWJ4 → fbG9cWB8 → XTQFWMJG → IGA3icWV → fSGCZWK8 → XNG7eWPG → XHG1kWVG → jHGDYWV4 → fLGDYWR8 → XLG5gWRG → bHG5gWVC → bPGDYWNC → PLG1kWRO → jG60lgW4 → lfaFWC72 → jYOGVOE4 → fKEmmXS8 → eYL4hRE9 → dVK5gSHA → bTE7eYJC → XPK9cSNG → TH81keVK → jWE8dYG4 → fVKFWSH8 → XHE7eYVG → XKHDYVSG → LHE7eYVS → XKE6fYSG → ZKH7eVSE → XLE7eYRGXKH5gVSGbHE7eYVCXPKDYSNGLH81keVSjWE6fYG4fZKFWSD8XMH7eVQGXHE3iYVGfKHDYVS8XLE7eYRG
968 max steps300000OOT → TOO2mjOOK → kP4mmmhN3 → jiPKmRN44 → ifO3miO75 → jdbGmVB94 → iaSKmRKC5 → hWG7meWG6 → gaOFmWOC7 → fUL7meRI8 → fXM8mdQF8 → eXOAmbOF9 → dUM8mdQIA → eTL7meRJ9 → fVL7meRH8 → fXN9mcPF8 → eWN9mcPG9 → dVM8mdQHA → eTM8mdQJ9 → eVK6mfSH9 → gWNAmbPG7 → fWL8mdRG8 → eXNAmbPF9 → dUM9mcQIA → dTK7meSJA → fUK8mdSI8 → eXL9mcRF9 → dVNBmaPHA → cSJ7meTKB → fTJ8mdTJ8 → eXK9mcSF9 → dVNCmZPHA → cRI7meULB → fTK8mdSJ8 → eXK8mdSF9 → eVOCmZOH9 → dSI6mfUKA → gVL9mcRH7 → fXL9mcRF8 → eWNBmaPG9 → dTK8mdSJA → eTK8mdSJ9 → eVK8mdSH9 → eVMAmbQH9 → dUK8mdSIA → eTL9mcRJ9dVJ7meTHAfUMBmaQI8eUI7meUI9fVMBmaQH8eUJ8mdTI9eVLAmbRH9dUK9mcSIAdTK9mcSJAdTJ8mdTJAeTK9mcSJ9dVJ8mdTHAeTMBmaQJ9dTH6mfVJAgVMBmaQH7fVJ8mdTH8eXMBmaQF9dTLAmbRJAcTI7meUJBfTKAmbSJ8eVI8mdUH9eVMCmZQH9dSI8mdUKAeTL9mcRJ9