Base 55: 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
28 max steps10 → 0s → r1 → p3 → l7 → dFNV7ldF
330 max steps100 → 0ss → rs1 → qs2 → ps3 → os4 → ns5 → ms6 → ls7 → ks8 → js9 → isA → hsB → gsC → fsD → esE → dsF → csG → bsH → asI → ZsJ → YsK → XsL → WsM → VsN → UsO → TsP → SsQ → RsRQsSRsR
424 max stepsS000 → RssR → RQRS → 1ssr → r0r2ro32pk74lcF8dMVGN8jWb8jIbIZIJGbaLGbYLCfYTCfQT2pQn2p6ngB6hUNCV6lOf6lEfQRER0rSr0r2
526 max steps30000 → 2sssq → q1sq3 → rms52 → qls63 → pjs84 → ogsB5 → ncsF6 → mXsK7 → lRsQ8 → kKsX9 → jPsSA → iJsYB → hOsTC → gIsZD → fNsUE → eHsaF → dMsVG → cGsbH → cKsXH → bHsaI → bIsZI → aIsZJ → aGsbJcHsaHbKsXIaGsbJ
691 max steps20009q → q91qj3 → pnZI54 → liGbA8 → dYKXKG → NECfeW → TQ8jSQ → b31qpI → pmIZ64 → lgGbC8 → dUKXOG → ND5mfW → hS8jQC → bV1qNI → pJ7kZ4 → ldFcF8 → dOMVUG → N95mjW → ha8jIC → bVHaNI → KI7kaZ → dIEdaG → PNHaVU → J84nka → jcGbGA → ZMKXWK → FD9ife → ZSOTQK → F51qne → piOTA4 → lY4nK8 → jdDeFA → ZRNURK → F6ssle → md6lF7 → geNUED → TQ6lSQ → f31qpE → pmQR64 → lg0rC8 → rdTOF2 → pO4nU4 → lj5m98 → hdZIFC → VOGbUO → L75mlY → heCfEC → VTPSPO → 742pom → nkeD86 → hcQRGC → VM0rWO → rA6li2 → pfXKD4 → lSCfQ8 → dT1qPG → pN3oV4 → mk7k87 → fdbGFE → ROKXUS → D60rmg → rgSPC2 → pU2pO4 → nl5m76 → igdECB → XUOTOM → B64nmi → jgWLCA → ZUAhOK → XF5mdM → hOAhUC → XV5mNM → hB7khC → dWUNMG → NA6liW → fY8jKE → bRDeRI → RIssZS → aR6lRJ → fGssbE → ec3oGF → lPLWT8 → dB3ohGlWMVM8dA8jiGbYMVKIJE8jeabQGbSILJ1qZYpGCfc4lTLWP8dB3ohG
747 max steps500000R → R4sssnS → oRPsSR5 → nP0srT6 → slNsU71 → rlNsU72 → qkNsU83 → piMsVA4 → ofLsWD5 → nbJsYH6 → mWHsaM7 → lVDseN8 → kYGsbK9 → jUGsbOA → iTCsfPB → hWFscMC → gSFscQD → fRBsgRE → hSDseQC → gUDseOD → fTFscPE → eQCsfSF → gQDseSD → fTDsePE → fREsdRE → eRBsgRF → hRCsfRC → gVDseND → fTGsbPE → ePBsgTF → hREsdRC → gTBsgPD → hTGsbPC → gRBsgRD → hTEsdPC → gTDsePD → fTEsdPE → eRDseRF → fPCsfTE → gRFscRDfRAshREiTDsePBhVEsdNCgTFscPDfRCsfREgRDseRDfTCsfPEgRFscRD
8206 max steps400005pp → pp53on34 → mmkhA867 → gfcWLGDD → TSMAhWQQ → XA31qpiM → pmYAhK64 → lgXDeLC8 → dURBgROG → VN5ssmVO → nVNssUN6 → mVQ0rSN7 → rf81qkD2 → qocRQG43 → nkM0rW86 → rhc9iGB2 → pZWLWMJ4 → lGB9ihc8 → dZWLWMJG → NGB9ihcW → ZWM8jWMK → bFA9iidI → ZYOIZUKK → HFE5medc → hQOKXUSC → VD61qmfO → pgS6lQC4 → lfU1qOD8 → pdS5mQF4 → lhO1qUB8 → pdW5mMF4 → lhO9iUB8 → dZW5mMJG → hNG9icVC → ZVM7kWNK → dFA7kidG → dYOMVUKG → NE95mjeW → haQ8jSIC → bVI1qaNI → pJI7kaZ4 → ldIFcaF8 → dONHaVUG → NJ85mkZW → hcG8jcGC → bVMLWWNI → JBA7kiha → dYWGbMKG → NLE9ieXW → ZQC8jgSK → bUF1qdOI → pOJ5mZU4 → lhG5mcB8 → hdWLWMFC → VOB9ihUO → ZW75mlMK → heF9idEC → ZVQNUSNK → F871qlke → pecOTGE4 → lQM4nWS8 → jdA1qiFA → pZYNUKJ4 → lGE6lec8 → fdQLWSFE → ROB1qhUS → pW60rmM4 → rlg9iC72 → peZTOJE4 → lQG4ncS8 → jdM1qWFA → pZO9iUJ4 → lZG5mcJ8 → hdMFcWFC → VON9iVUO → Z875mlkK → hecEdGEC → VQPLWTSO → B741qoli → pkeWLE84 → lcQAhSG8 → dXM1qWLG → pNC9igV4 → lZU7kOJ8 → ecG5mcGF → hPMLWWTC → VBA3oihO → lYW6lMK8 → fdE9ieFE → ZRQNUSRK → F71ssqle → rlb6lH72 → pfeJYED4 → lSQEdSQ8 → dP21qqTG → poN3oV44 → mkk7k887 → fdcbGGFE → ROMKXWUS → DA60rmig → rgYSPKC2 → pUE2peO4 → nlQ5mS76 → ige1qECB → pXUPSOL4 → lC62pmg8 → ngdTOFC6 → hUO4nUOC → jV65mmNA → hgZ7kJCC → dVUFcONG → OM85mkWV → hcA6liGC → fYVLWNKE → REB7kheS → dWQ0rSMG → rNA1qiV2 → qoY7kK43 → nkdDeF86 → hcRNURGC → VM6sslWO → mWN0rVM7 → rfA7kiD2 → pdYRQKF4 → lOE0reU8 → rdQ5mSF2 → phO1qUB4 → plW5mM74 → lhe9iEB8 → dZWPSMJG → NGA2picW → nYM8jWK6 → hbE9ieHC → ZVQJYSNK → GE81qked → pcQMVSG4 → lM91qjW8 → pda9iIF4 → lZOHaUJ8 → dJG5mcZG → hNMFcWVC → VNA7kiVO → dY86lkKG → fcNDeVGE → SQM7kWSR → dA20rqiG → roYMVK42 → pkE8je84 → lcbPSHG8 → dMK2pYWG → nNE9ieV6 → hZQ7kSJC → dVG1qcNG → pNM7kWV4 → ldA7kiF8 → ecYNUKGF → PME6leWU → fQA4niSE → jYR1qRKA → pZDsseJ4 → ofW4nMD5 → kiS9iQA9 → bZY1qKJI → pJGDecZ4 → lRMFcWR8 → dN9ssiVG → jcL7kXGA → dZMBgWJG → VNG9icVO → ZM86lkWK → fcF9idGE → ZROLWURK → FB5ssmhe → nhX2pLB6 → nhWBgMB6 → hWV9iNMC → ZVA7kiNK → dYF7kdKG → dONDeVUG → RN85mkVS → hc80rkGC → rcVLWNG2 → pMB7khW4 → ldW9iMF8 → dZO9iUJGZNG5mcVKhMF7kdWCdVO9iUNGZN85mkVKhcF7kdGCdVOLWUNGNB85mkhWhcW8jMGCbVM9iWNIZJA7kiZKdYGEdcKGPNMDeWVURA84nkiSjcY0rKGArZMDeWJ2pRG9icR4lZLssWJ8kZQ2pSJ9nbG1qcH6phMJYWB4lWF9idM8dZO9iUJG