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 steps1 → 0 → 0
213 max steps10 → 0m → l1 → j3 → f7 → XF → HV → DZ → LR → 5h → bB → PN → 1l → j3
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 → OmO → NmP → OmO
425 max stepsP000 → OmmO → ONOP → 1mml → l0l2 → li32 → je74 → fWF8 → XGVG → HEXW → JEXU → JAbU → RAbM → R4hM → d4hA → dSJA → T8dK → V8dI → VCZI → NCZQ → N2jQ → h2j6 → haB6 → bONC → P0lO → l0l2
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 → WEmXH → YFmWF → XImTG → WEmXH
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 → jfXE74 → fYITE8 → XKAbSG → RH7eVM → XE4hYG → dKGVSA → TF7eXK → XI8dUG → VHBaVI → PECZYO → NK0lSQ → l82je2 → jhVG54 → fcEXA8 → XSITKG → HB7ebW → XQEXMG → JH3iVU → fEAbY8 → XRJSLG → H95gdW → bUEXIC → PJBaTO → PA0lcO → lS0lK2 → lj7e32 → jgWF64 → faGVC8 → XOEXOG → JGmmVU → WT0lJH → lF9cX2 → jTHUJ4 → fD9cZ8 → XTLQJG → HA4hcW → dSEXKA → TJ7eTK → XA8dcG → VSGVKI → FD7eZY → XMITQG → HB3ibW → fQEXM8 → XJ3iTG → fH9cV8 → XTDYJG → LH9cVS → TE6fYK → ZK8dSE → VL7eRI → XD5gZG → bMGVQC → PF3iXO → fI0lU8 → lXBaF2 → jPHUN4 → fD1kZ8 → jXLQF4 → fI4hU8 → dXBaFA → TPHUNK → D91kda → jUMPI4 → fC2ja8 → hXNOF6 → bI0lUC → lPBaN2 → jP1kN4 → jf1k74 → jfXE74
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 → aPBmaND → bNCmZPC → aPBmaND
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 → XLE7eYRG → XKH5gVSG → bHE7eYVC → XPKDYSNG → LH81keVS → jWE6fYG4 → fZKFWSD8 → XMH7eVQG → XHE3iYVG → fKHDYVS8 → XLE7eYRG
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 → eTL9mcRJ9 → dVJ7meTHA → fUMBmaQI8 → eUI7meUI9 → fVMBmaQH8 → eUJ8mdTI9 → eVLAmbRH9 → dUK9mcSIA → dTK9mcSJA → dTJ8mdTJA → eTK9mcSJ9 → dVJ8mdTHA → eTMBmaQJ9 → dTH6mfVJA → gVMBmaQH7 → fVJ8mdTH8 → eXMBmaQF9 → dTLAmbRJA → cTI7meUJB → fTKAmbSJ8 → eVI8mdUH9 → eVMCmZQH9 → dSI8mdUKA → eTL9mcRJ9