Base 50: 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
210 max steps20 → 1m → k3g7YFIVCbOP0nm1k3
327 max steps100 → 0nn → mn1 → ln2 → kn3 → jn4 → in5 → hn6 → gn7 → fn8 → en9 → dnA → cnB → bnC → anD → ZnE → YnF → XnG → WnH → VnI → UnJ → TnK → SnL → RnM → QnN → PnO → OnPOnP
417 max steps600P → P5hP → bnnC → bBbD → QNPO → 30ml → mh52 → kbB4gPN8Y1lGkHV4gDZ8YLRGI5hWcDZCQLRO61likbB4
527 max stepsO0000 → NnnnQ → QMnQO → R1nlN → mNnP2 → lOnO3 → kMnQ4 → jNnP5 → iLnR6 → hMnQ7 → gKnS8 → fLnR9 → eJnTA → dKnSB → cInUC → bJnTD → aHnVE → ZInUF → YGnWG → XHnVH → WFnXI → YEnYG → ZHnVF → YHnVGXGnWHXFnXHYFnXGYHnVG
6143 max steps30000J → J2nnkV → lUEYJ3 → iKAcT6 → cS8eLC → WQ6gNI → aE2kZE → iMKSR6 → c84ifC → eXPNGA → UH1lWK → kF9dY4 → gUIUJ8 → YCAcbG → SPHVOM → E60mha → mbLRC2 → kP5hO4 → gc0mB8 → mYQMF2 → kJ3jU4 → hfAc87 → aXRLGE → MH5hWS → cF5hYC → cQIUNC → QC2kbO → iP1lO6 → kc0mB4 → mgQM72 → kZ3jE4 → hfKS87 → aX7fGE → YMGWRG → IG4iXW → eHDZWA → UMEYRK → KA4idU → eT9dKA → VT8eKJ → WC8ebI → WPDZOI → ME0mZS → mL5hS2 → kc6gB4 → gaQMD8 → YN3jQG → gI2kV8 → iYCaF6 → cOIUPC → QC0mbO → mP1lO2 → lj0m43 → mie852 → kdVHA4 → gTDZK8 → YM8eRG → WI4iVI → eECaZA → UOKSPK → A80mfe → mXTJG2 → kH9dW4 → gUEYJ8 → YKAcTG → SI8eVM → WD5haI → cNDZQC → QM2kRO → i51li6 → kdbBA4 → gTPNK8 → Y91leG → kVHVI4 → gECaZ8 → YOKSPG → I80mfW → mXDZG2 → kMGWR4 → gG4iX8 → eYGWFA → UJFXUK → IB9dcW → URDZMK → MA4idS → eT5hKA → cU8eJC → WQAcNI → SE2kZM → iL5hS6 → db6gCB → aSOOLE → M6nngS → hRDZM7 → aM4iRE → eM4iRA → eU4iJA → eUAcJA → USAcLK → SA6gdM → aT5hKE → cM8eRC → WQ4iNI → eE2kZA → iUKSJ6 → cB7fcC → YRPNMG → I51liW → kdDZA4 → gTLRK8 → Y95heG → cVHVIC → QECaZO → OL1lSQ → k71lg4 → kgYE74 → gZJTE8 → YL9dSG → UI6gVK → aD9daEUNLRQKA62kheibTJC6cP9dOCUQ0mNKmA2kd2kiSK54gd7fA8ZXSKGFKH7fWUYF9dYGUJHVUKEB9dcaURLRMKA64iheebTJCAUP9dOKUA0mdKmT9dK2kU8eJ4gWAcH8YSEYLGKI6gVUaD9daE
732 max stepsC0000OP → POBnbPP → cCnnnaC → bbCnaCD → bPNnPOD → aE0nmZE → nYLnRF1 → mYCnaF2 → laKnSD3 → kYFnXF4 → jVInUI5 → iRCnaM6 → hWDnZH7 → gUHnVJ8 → fPBnbO9 → eUCnaJA → dSGnWLB → cNAncQC → dQEnYNB → cPAncOC → dQDnZNB → cQBnbNC → cQDnZNC → bPBnbOD → cOCnaPC → bQBnbND → cODnZPC → bPAncOD → dPCnaOBcRBnbMCcQEnYNCbOAncPDdPCnaOB
8611 max steps500009EJ → JE94ieZV → eVLBbSIA → UQD6gaNK → aNA2kdQE → iTM2kRK6 → ic94ieB6 → ecVQMIBA → URD3jaMK → gNA4idQ8 → eYT2kKFA → iUJ8eUJ6 → cWBAccHC → SRQEYNMM → K652kihU → idb9dCA6 → cUTOOKJC → QB8nnecO → fcGBbXB9 → WRQGWNMI → GE52kiZY → idLHVSA6 → cTE6gZKC → aQL8eSNE → WM72kgRI → iZE4iZE6 → ecLKSSBA → UR86gfMK → aXA4idGE → eTMGWRKA → UG94ieXK → eVH9dWIA → VTFCaYKJ → OJC8ebUQ → WPB1lcOI → kRE0mZM4 → mgL4iS72 → keZ6gE94 → gaVKSID8 → YND7faQG → YNI2kVQG → iID2kaV6 → icNCaQB6 → cRO2kPMC → iQ50miN6 → mdc2kBA2 → kiTQMK54 → gd93jeA8 → gYVSKIF8 → YJD7faUG → YNIAcVQG → SID2kaVM → iND5haQ6 → dbN2kQCB → iSP2kOL6 → ic70mgB6 → mcZQMEB2 → kRL3jSM4 → hf74ig87 → eaZWGEDA → UNLFXSQK → IA72kgdW → iZTDZKE6 → cML8eSRC → WQ74igNI → eZE2kZEA → iULKSSJ6 → cB86gfcC → aXRPNMGE → MH51liWS → kdF5hYA4 → gcTIUKB8 → YRC8ebMG → WPI4iVOI → eED0maZA → mUNKSQJ2 → kB82kfc4 → igXQMG76 → cZH3jWEC → gQLEYSN8 → YK72kgTG → iZI8eVE6 → cWLCaSHC → QOF6gYPO → aJ20mlUE → mjMAcR42 → kfS4iL84 → geX6gG98 → aYVGWIFE → MJGCaXUS → OHB5hcWQ → cRF1lYMC → kQJ4iUN4 → geB2kc98 → iYVQMIF6 → cJD3jaUC → gQNAcQN8 → YS32kkLG → ihI6gV66 → cbaCaDCC → QPOMQPOO → 4210mmlk → mljf7422 → kjfXF844 → gfXHVG88 → YXHDZWGG → MIHEYWVS → KFD5haYU → cNJ9dUQC → UQB2kcNK → iRA2kdM6 → icT4iKB6 → ecR8eMBA → WUR4iMJI → eEB4icZA → eURKSMJA → UB84ifcK → eXR9dMGA → VTH4iWKJ → eFC8ebYA → WUPIUOJI → ECB0mcba → mRPLROM2 → k650mih4 → mgdaCA72 → kZTNPKE4 → gL91leS8 → kYV6gIF4 → gaJCaUD8 → YONAcQPG → SI30mkVM → mhD5ha62 → kcbMQCB4 → gRP3jOM8 → gY50miF8 → mdYIUFA2 → kTJBbUK4 → gQB8ecN8 → YWR2kMHG → iIF4iYV6 → ecJCaUBA → UROAcPMK → SA50midM → mdT5hKA2 → kcT8eKB4 → gWR8eMH8 → YWF4iYHG → eJIEYVUA → UKDAcaTK → SNA8edQM → WT62khKI → ibE8eZC6 → cWPKSOHC → QF80mfYO → mXJ1lUG2 → ljHAcW43 → ifSEYL86 → cXK6gTGC → aQH8eWNE → WMF2kYRI → iJE4iZU6 → ecLAcSBA → USR6gMLK → aA74igdE → eZTLRKEA → UL95heSK → cVA6gdIC → aTQCaNKE → OM92keRQ → iV51liI6 → kdcCaBA4 → gTRNPMK8 → Y951lieG → kdVHVIA4 → gTECaZK8 → YOL8eSPG → WI70mgVI → mZECaZE2 → kOLKSSP4 → g870mgf8 → mZYWGFE2 → kLJFXUS4 → gIB6gcV8 → aYRCaMFE → OMJ4iURQ → eB51licA → kdUQMJA4 → gTB3jcK8 → gYR8eMF8 → YWJ4iUHG → eIFAcYVA → USJCaULK → OBA6gdcQ → aTR1lMKE → kM94ieR4 → geV4iI98 → eYVCaIFA → UOJCaUPK → OBA0mdcQ → mTR1lMK2 → lj94ie43 → ifeUI986 → cXVBbIGC → RPHCaWON → OF40mjYQ → mfJ1lU82 → ljXAcG43 → ifSGWL86 → cXG6gXGC → aQHGWWNE → MGF2kYXS → iJH5hWU6 → dbFAcYCB → TRPIUOML → C850mifc → mdXPNGA2 → kTH1lWK4 → kgF8eY74 → gZWIUHE8 → YLFBbYSG → QJI6gVUO → aDB1lcaE → kRNLRQM4 → g652kih8 → idbXFCA6 → cTPHVOKC → QE90meZO → mVL1lSI2 → ljD6ga43 → ifaMQD86 → cXN3jQGC → gQH2kWN8 → iYF2kYF6 → icJIUUB6 → cRCAcbMC → SQP4iONM → e630mkhA → mhbTJC62 → kbP9dOC4 → gUP0mOJ8 → mYB0mcF2 → mkRIUM32 → khC4ib64 → gebOOC98 → YVOnnOIG → XVA6gdIH → aTGCaXKE → OMH8eWRQ → WF51liYI → kdJDZUA4 → gTMAcRK8 → YS94ieLG → eVI6gVIA → aUDCaaJE → ONMAcRQQ → S531lkiM → khd5hA64 → gcbSKCB8 → YRP7fOMG → YI50miVG → mdICaVA2 → kTOCaPK4 → 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
969 max stepsI00000XXa → aXXHnVGGE → ZKHFnXWTF → YKGBnbXTG → cLICnaVSC → bQI9ndVND → eQJ7nfUNA → gVL6ngSI8 → hYO9ndPF7 → gYO9ndPF8 → fXO9ndPG9 → eWN8neQHA → fUN8neQJ9 → fWL6ngSH9 → hXOAncPG7 → gXM8neRG8 → fYOAncPF9 → eVN9ndQIA → eUL7nfSJA → gVL8neSI8 → fYM9ndRF9 → eWOBnbPHA → dTK7nfTKB → gUJ8neUJ8 → fYLAncSF9 → eVNCnaQIA → dSI7nfVLB → gUL9ndSJ8 → fXK8neTG9 → fWOCnaPH9 → eTJ7nfUKA → gVL9ndSI8 → fXL9ndSG9 → eWNBnbQHA → dTK8neTKB → fTJ8neUK9 → fWL9ndSH9 → eWMAncRHA → dUL9ndSJB → eSK8neTLA → fUK7nfTJ9 → gWM9ndRH8 → fXM9ndRG9 → eWNAncQHA → dUL8neSJB → fTK8neTK9 → fWK8neTH9 → fWNBnbQH9 → eUK8neTJAfUL9ndSJ9eWK8neTHAfUNBnbQJ9eUI6ngVJAhWMBnbRH7gWK9ndTH8fXMBnbRG9eULAncSJAdUJ8neUJBfTKAncTK9eVI8neVIAfUMCnaRJ9eTH7nfWKAgVNBnbQI8fVJ7nfUI9gWNBnbQH8fVK8neTI9fWMAncRH9eVL9ndSIAeUL9ndSJAeUK8neTJA