Base 48: Maximum Iteration Sequences: Full Cycle

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
Full Cycle
12 max steps100
223 max steps20 → 1k → i3e7WFGVEXITAbQL4hc9SJ8dUHCZMP2jg5aBON0lk1i3
326 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 → NlONlO
421 max steps3006 → 62ig → gZB6 → aNNC → NllO → OMOO → 1llk → k0k2 → kh32 → id74 → eVF8 → WFVGHEWVIDXUKBZSO7dOVllGVFVHGDXWKFVSG7dWWFVG
524 max steps10006 → 60lkg → ldl71 → kdl72 → jcl83 → ialA4 → hXlD5 → gTlH6 → fOlM7 → eIlS8 → dLlP9 → cHlTA → bKlQB → aGlUC → ZJlRD → YFlVE → XIlSF → WElWG → XFlVF → WHlTG → VElWH → XElWF → XHlTF → WFlVGWFlVG
6103 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 → YJFVSEKG8cVSUF7dWIWHBZUGOGCYVOMEllWQXP5fMFaI2iTCgOAaN6aQ0kLCkO4gN2ic0k94keSI72iX9bE4eSISJ8WA8cbGURFVKIGC6eZWYNFVOEKG0kVSkF7dW2iWGUF4eHDXU8WKCYRGMG6eVQYF3hWEeKGUR8WE6eXGYJFVSE
739 max stepsN000000 → MlllllP → PLlllPN → QOLlPNM → Q41ljhM → kfKlQ62 → jeKlQ73 → icJlR94 → hZIlSC5 → gVGlUG6 → fQElWL7 → eRAlaK8 → dUFlVH9 → cODlXNA → bP9lbMB → cQElWLA → bOAlaNB → bQClYLB → aPClYMC → ZOBlZND → aMBlZPCaOClYNCZOAlaNDbNBlZOBaQBlZLCaODlXNCZN9lbODcOBlZNAbRBlZKBaQElWLCZMAlaPDbNClYOBaPAlaMCbODlXNBaO9lbNCcPClYMAbQBlZLBaQDlXLCZNBlZODaMBlZPC
8361 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 → 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
948 max stepsF00000HHN → NHHElWUUP → XFD6leYWF → fRJHlTSK7 → eOA7ldbN8 → eWTDlXIF8 → dRIDlXTK9 → cQF8lcWLA → dSNAlaOJ9 → cTH4lgUIA → hWLBlZQF5 → gWKAlaRF6 → fWLBlZQF7 → eUKAlaRH8 → dUJ9lbSH9 → cUKAlaRHA → bSJ9lbSJB → cQI8lcTLA → dSK7ldRJ9 → eUK7ldRH8 → eWM9lbPF8 → dVM9lbPG9 → cUL8lcQHA → dSL8lcQJ9 → dUJ6leSH9 → fVMAlaPG7 → eVK8lcRG8 → dWMAlaPF9 → cTL9lbQIA → cSJ7ldSJA → eTJ8lcSI8 → dWK9lbRF9cUMBlZPHAbRI7ldTKBeSJ8lcSJ8dWJ8lcSF9dUNClYOH9cRH6leUKAfUL9lbQH7eWK8lcRF8dWNBlZOF9cSK8lcRJAdSJ7ldSJ9eUK8lcRH8dWL9lbQF9cUMAlaPHAbSJ7ldSJBeSI8lcTJ8dWK9lbRF9