Base 49: 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
23 max steps10 → 0m → l1 → j3
325 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
44 max stepsP000 → OmmO → ONOP → 1mml → l0l2
523 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
656 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
732 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
8139 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
945 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