Base 50: 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
22 max steps20 → 1m → k3
326 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 → OnP
47 max steps600J → J5hV → cBbC → ROON → 3nnk → k2k4 → if76 → cXFC
523 max stepsO0000 → NnnnQ → QMnQO → R1nlN → mNnP2 → lOnO3 → kMnQ4 → jNnP5 → iLnR6 → hMnQ7 → gKnS8 → fLnR9 → eJnTA → dKnSB → cInUC → bJnTD → aHnVE → ZInUF → YGnWG → XHnVH → WFnXI → YEnYG → ZHnVF → YHnVG
6119 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 → aD9daE
728 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 → dPCnaOB
8262 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 → gO90meP8
948 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 → eUK8neTJA