Base 55: 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
25 max steps10 → 0s → r1 → p3 → l7 → dF
328 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 → RsR
44 max stepsS000 → RssR → RQRS → 1ssr → r0r2
523 max steps30000 → 2sssq → q1sq3 → rms52 → qls63 → pjs84 → ogsB5 → ncsF6 → mXsK7 → lRsQ8 → kKsX9 → jPsSA → iJsYB → hOsTC → gIsZD → fNsUE → eHsaF → dMsVG → cGsbH → cKsXH → bHsaI → bIsZI → aIsZJ → aGsbJ
682 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 → dB3ohG
739 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 → gRFscRD
8184 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 → dZO9iUJG