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 steps1 → 0 → 0
28 max steps10 → 0s → r1 → p3 → l7 → dF → NV → 7l → dF
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 → RsR → QsS → RsR
424 max stepsS000 → RssR → RQRS → 1ssr → r0r2 → ro32 → pk74 → lcF8 → dMVG → N8jW → b8jI → bIZI → JGba → LGbY → LCfY → TCfQ → T2pQ → n2p6 → ngB6 → hUNC → V6lO → f6lE → fQRE → R0rS → r0r2
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 → aGsbJ → cHsaH → bKsXI → aGsbJ
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 → dB3ohG → lWMVM8 → dA8jiG → bYMVKI → JE8jea → bQGbSI → LJ1qZY → pGCfc4 → lTLWP8 → dB3ohG
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 → gRFscRD → fRAshRE → iTDsePB → hVEsdNC → gTFscPD → fRCsfRE → gRDseRD → fTCsfPE → gRFscRD
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 → dZO9iUJG → ZNG5mcVK → hMF7kdWC → dVO9iUNG → ZN85mkVK → hcF7kdGC → dVOLWUNG → NB85mkhW → hcW8jMGC → bVM9iWNI → ZJA7kiZK → dYGEdcKG → PNMDeWVU → RA84nkiS → jcY0rKGA → rZMDeWJ2 → pRG9icR4 → lZLssWJ8 → kZQ2pSJ9 → nbG1qcH6 → phMJYWB4 → lWF9idM8 → dZO9iUJG