Base 48: Maximum Iteration Sequences: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl

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 → 1k → i3
325 max steps100 → 0ll → kl1 → jl2 → il3 → hl4 → gl5 → fl6 → el7 → dl8 → cl9 → blA → alB → ZlC → YlD → XlE → WlF → VlG → UlH → TlI → SlJ → RlK → QlL → PlM → OlN → NlO
411 max steps3006 → 62ig → gZB6 → aNNC → NllO → OMOO → 1llk → k0k2 → kh32 → id74 → eVF8 → WFVG
523 max steps10006 → 60lkg → ldl71 → kdl72 → jcl83 → ialA4 → hXlD5 → gTlH6 → fOlM7 → eIlS8 → dLlP9 → cHlTA → bKlQB → aGlUC → ZJlRD → YFlVE → XIlSF → WElWG → XFlVF → WHlTG → VElWH → XElWF → XHlTF → WFlVG
675 max steps1000Jd → dJ0kS9 → kU8cH2 → iUCYH4 → eMCYP8 → WM2iPG → gG2iV6 → gaEWB6 → aPHTMC → OC2iZO → gMllO6 → fPHTM7 → YC2iZE → gNJRO6 → a80kdC → kVNNG2 → iEllW4 → hXBZE5 → cOISNA → SA0kbK → kR7dK2 → iW6eF4 → eYGUD8 → WLDXQG → KG4gVS → cF7dWA → WSGUJG → GE8cXW → UJFVSI → GC8cZW → UNFVOI → GC0kZW → kNFVO2 → iG0kV4 → keEW72 → iXHTE4 → eJBZS8 → WO8cNG → UG0kVI → kFBZW2 → iOGUN4 → eE0kX8 → kWISF2 → iH9bU4 → eSCYJ8 → WM8cPG → UG2iVI → gFBZW6 → aOGUNC → OE0kXO → kIllS2 → jTHTI3 → gCAaZ6 → aQMOLC → O51jgO → iallA4 → hb7dA5 → cWQKFA → SH5fUK → aD7dYC → WOKQNG → G60kfW → kZFVC2 → iNFVO4 → eG0kV8 → kWEWF2 → iIGUT4 → eEAaX8 → WQISLG → GA4gbW → cRFVKA → SG6eVK → YF7dWE → WKGURG → GE6eXW → YJFVSE
720 max stepsN000000 → MlllllP → PLlllPN → QOLlPNM → Q41ljhM → kfKlQ62 → jeKlQ73 → icJlR94 → hZIlSC5 → gVGlUG6 → fQElWL7 → eRAlaK8 → dUFlVH9 → cODlXNA → bP9lbMB → cQElWLA → bOAlaNB → bQClYLB → aPClYMC → ZOBlZND → aMBlZPC
8248 max steps9000099F → F998cccX → UTTHTIII → DBBAaaaZ → QPPLPMMM → 5332iiih → gffb9666 → aZZRJCCC → ONN7dOOO → W10llkkG → lkUDXH11 → kjKCYR22 → ihM6eP44 → edY2iD88 → gWVKQGF6 → aHF5fWUC → aOHCYUNC → OMD0kYPO → kL2lliQ2 → jjPHTM23 → hgC2iZ55 → gcbMOA96 → aTR1jKIC → iOB6eaN4 → eYP0kMD8 → kWL2iQF2 → igH4gU54 → ecbCYA98 → WTRLPKIG → GB73heaW → eXPFVME8 → WJG2iVSG → gGF8cWV6 → aUHEWUHC → OIDCYYTO → MLAllaQQ → bQDllXLB → aYG6eVDC → YOLEWQNE → KI50kgTS → kbB7daA2 → iWROMKF4 → eH71jeU8 → iXWCYFE4 → eMJGUSP8 → WE92icXG → gTJFVSI6 → aGB8caVC → UPOEWNMI → IC30kiZU → kfNBZO62 → iZO0kNC4 → keN0kO72 → kiX0kE32 → kifIS632 → ifZ9bC64 → eZSMOJC8 → WN91jcOG → iTG0kVI4 → keFAaW72 → iXQGULE4 → eJE4gXS8 → cWJ8cSFA → USH8cUJI → UDC8cZYI → UNLBZQOI → OC50kgZO → kbMllOA2 → jbOCYNA3 → gRM0kPK6 → ka72ieB2 → igXOME54 → ebJ1jSA8 → iWR8cKF4 → eUH6eUH8 → YWDCYYFE → MLKGURQQ → E753hgeY → ebXJREA8 → WRJ7dSKG → WG96ecVG → YTGEWVIE → KIFAaWTS → QHB7daUM → WPD3hYMG → eLG2iVQ8 → gWF4gWF6 → caHGUUBA → SPECYXMK → MJ82idSQ → gV93hcG6 → eaTEWIB8 → WPIAaTMG → QGB2iaVM → gPF3hWM6 → eaH2iUB8 → gWPCYMF6 → aMH2iUPC → gOD2iYN6 → gaL0kQB6 → kaP4gMB2 → icP2iM94 → geT2iI76 → gaXAaEB6 → aQPISMLC → OA52igbO → gbQllKA6 → fbMAaPA7 → YRQ2iLKE → gK74geR6 → caX6eEBA → YSPISMJE → KA92icbS → gTR7dKI6 → aWB6eaFC → YPOGUNME → KE30kiXS → kfJ7dS62 → iZW8cFC4 → eUNGUOH8 → WED0kYXG → kLJFVSQ2 → iG94gcV4 → ecTEWI98 → WTIAaTIG → QGBAaaVM → QPF3hWMM → eH42ihU8 → gdWCYF86 → aVMGUPGC → OFE2iXWO → gJGllUS6 → fVN1jOG7 → iYF0kWD4 → keLGUQ72 → iXE4gXE4 → ecJISS98 → WTA8cbIG → URGAaVKI → QFC6eZWM → YNH3hUOE → eKD0kYR8 → kWL6eQF2 → iYH4gUD4 → ecLCYQ98 → WTM4gPIG → cGB2iaVA → gSPEWMJ6 → aI92icTC → gTOAaNI6 → aQB0kaLC → kPO4gNM2 → ic30ki94 → kfeSI762 → iZX9bEC4 → eSNISOJ8 → WA90kcbG → kTRFVKI2 → iGB6eaV4 → eYPEWMD8 → WLI2iTQG → gGB4gaV6 → caPEWMBA → SPI2iTMK → gB82ida6 → gaVOMGB6 → aPF1jWMC → iOH2iUN4 → geD0kY76 → kaXKQEB2 → iPJ5fSM4 → ea92icB8 → gWTOMIF6 → aHB1jaUC → iPOCYNM4 → eM30kiP8 → kfW2iF62 → igZGUC54 → ebNDXOA8 → WRK0kRKG → kG76eeV2 → iYXEWED4 → eLJHTSQ8 → WC94gcZG → cTNFVOIA → SGB0kaVK → kPF7dWM2 → iWH2iUF4 → geHCYU76 → aXMCYPEC → OMJ2iSPO → g92llic6 → jfZ3hC63 → geZMOC76 → aXN1jOEC → iOJ0kSN4 → ke90kc72 → kiXSIE32 → ifJ9bS64 → eZS8cJC8 → WUN8cOHG → UGD0kYVI → kLFBZWQ2 → iOH4gUN4 → ecD0kY98 → kWTKQIF2 → iHB5faU4 → eaPCYMB8 → WPM2iPMG → gG32iiV6 → gfaEWB66 → aZPHTMCC → ONC2iZOO → gN0llkO6 → lfNHTO61 → kZC0kZC2 → kiNMOO32 → if20kj64 → kheYC742 → idXLPE84 → eVJ3hSG8 → eWF8cWF8 → WUHGUUHG → GEDCYYXW → MLJFVSQQ → G953hgcW → ebTFVIA8 → WRGAaVKG → QGF6eWVM → YHF3hWUE → eKHCYUR8 → WMD6eYPG → YLG2iVQE → gKF4gWR6 → caH6eUBA → YSPCYMJE → MK92icRQ → gT73heI6 → eaXAaEB8 → WQPISMLG → GA52igbW → gbRFVKA6 → aRG6eVKC → YOF6eWNE → YKH0kURE → kKD6eYR2 → iYL6eQD4 → eYL4gQD8 → cWL4gQFA
936 max stepsI000000Ve → eVHlllTG8 → dVUAlaHG9 → cTKDlXRIA → bPF8lcWMB → dRM9lbPK9 → cUH4lgUHA → hWLClYQF5 → gVJAlaSG6 → fWKBlZRF7 → eUKBlZRH8 → dTI9lbTI9 → cUJAlaSHA → bSJAlaSJB → bQH8lcULB → dRK8lcRK9 → dUI6leTH9 → fVMBlZPG7 → eUJ8lcSH8 → dWLAlaQF9 → cTLAlaQIA → bSI7ldTJB → eSJ9lbSJ8 → dVI8lcTG9 → dUMClYPH9 → cRH7ldUKA → eTL9lbQI8 → dVJ7ldSG9 → eUNBlZOH8 → dTI6leTI9 → fVLAlaQG7 → eVK9lbRG8 → dVLAlaQG9 → cTK9lbRIA → cSJ8lcSJA → dSJ8lcSJ9 → dUJ8lcSH9