Base 51: 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
24 max steps10 → 0o → n1 → l3 → h7
326 max steps100 → 0oo → no1 → mo2 → lo3 → ko4 → jo5 → io6 → ho7 → go8 → fo9 → eoA → doB → coC → boD → aoE → ZoF → YoG → XoH → WoI → VoJ → UoK → ToL → SoM → RoN → QoO → PoP
44 max stepsQ000 → PooP → POPQ → 1oon → n0n2
525 max stepsP0000 → OoooQ → QNoQP → R0onO → oOoP1 → nPoO2 → mOoP3 → lNoQ4 → kNoQ5 → jMoR6 → iMoR7 → hLoS8 → gLoS9 → fKoTA → eKoTB → dJoUC → cJoUD → bIoVE → aIoVF → ZHoWG → YHoWH → XGoXI → YEoZH → aHoWF → ZIoVG → YGoXH
6119 max steps5000Ce → eC4jcB → fTPOLA → V80ngK → nYAdG2 → lTHWL4 → hF7gZ8 → aYJUGF → LIAdWU → TE8faM → XM6hSI → bF5iZE → dNJURC → RB3kdO → hS2lM8 → jZ5iF6 → ecJUCB → TQAdOM → T71mhM → la6hE4 → hbLSD8 → ZO6hQG → bJ1mVE → lNBcR4 → hR3kN8 → hZ3kF8 → hZJUF8 → ZKAdUG → TJ9eVM → VC6hcK → bQAdOE → TN1mRM → l73kh4 → igZE87 → bYKTGE → NI8fWS → XE4jaI → fMEZSA → VL5iTK → dB7gdC → ZSQNMG → J62liW → jcCbC6 → dQOPOC → R20nmO → nk2l42 → ljf854 → heWHA8 → ZUEZKG → LJ9eVU → VC8fcK → XQAdOI → TF1mZM → lK6hU4 → hb9eD8 → ZVNQJG → JC2lcW → jQCbO6 → dP1mPC → lQooN4 → kRKTN5 → f93kfA → hWUJI8 → ZEAdaG → TMIVSM → D75ihc → daOPEC → RM0nSO → n62li2 → ljbC54 → heOPA8 → ZU0nKG → nJ9eV2 → lVBcJ4 → hRBcN8 → ZR3kNG → hJ3kV8 → hZBcF8 → ZRJUNG → JB3kdW → hSCbM8 → ZP5iPG → dIooVC → cW7gID → ZPDaPG → NIooVS → WR2lNJ → jD3kb6 → hdNQB8 → ZS2lMG → jJ5iV6 → ecBcCB → TRPONM → 740nki → ngaD82 → lYMRG4 → hI4jW8 → fZDaFA → VNJURK → CA3ked → hUQNK8 → ZA2leG → jUIVK6 → dD9ebC → VRNQNK → B42lke → jgSL86 → dY6hGC → bRHWNE → NF3kZS → hK4jU8 → fZ9eFA → WUJUKJ → DB9edc → VSOPMK → B60nie → ncSLC2 → lQ6hO4 → hb1mD8 → lZNQF4
738 max stepsQ000000 → PoooooP → POoooPQ → QPOoPPP → Q0ooonP → oPNoQP1 → nR0onN2 → olPoO31 → nlMoR32 → mkOoP43 → liLoS64 → kfMoR95 → jbIoVD6 → iWIoVI7 → hQDoaO8 → gUBocK9 → fVHoWJA → eOCobQB → dSCobMC → cREoZND → bOBocQE → dOCobQC → cRCobND → cPDoaPD → bPAodPE → ePBocPB → dTCobLC → cRFoYND → bNAodRE → ePDoaPB → dRAodNC → eRFoYNB → dPAodPC → eRDoaNB → dRCobNC → cRDoaND → bPCobPE → cNBocRD → dPEoZPC
8201 max stepsM0000Zee → eeZLSFAB → UTK6hULL → bA97gfeE → ZWUMRKIG → JEA4jeaW → fUMCbSKA → VPA5iePK → dUAoodKC → ecJ8fVCB → XTQBcOLI → RF81mgZO → lYK2lUG4 → jhI9eW76 → daVDaJEC → RNMBcSRO → R642lkiO → jgc2lC86 → jdYPOGB6 → dSI0nWMC → nRE5iaN2 → ldM3kSB4 → igS5iM87 → dbY5iGDC → dROHWQNC → RF41mkZO → lgK2lU84 → jhY9eG76 → daVHWJEC → RMFBcZSO → RK62liUO → jcA2leC6 → jdUPOKB6 → dSA0neMC → nUR5iNK2 → ldA3keB4 → igURMK87 → bYA4jeGE → fUNHWRKA → VFA3keZK → hUKAdUK8 → ZTA9eeLG → VUJ7gVKK → ZCB9edcG → VSQIVOMK → DB61midc → lcSOPMC4 → hQ60niO8 → ncZ1mFC2 → mkQJUO43 → jgB1md86 → ldYRMGB4 → hSI4jWM8 → fZE5iaFA → dVMJUSJC → RCB5idcO → dSQ2lOMC → jR61miN6 → ldc3kCB4 → igSPOM87 → bY60niGE → ncNHWRC2 → lQF3kZO4 → igK1mU87 → lbY9eGD4 → hVOHWQJ8 → ZFC1mcZG → lQKIVUO4 → hDA1meb8 → lZUNQKF4 → hKA2leU8 → jZU9eKF6 → dVK9eUJC → VRC9ecNK → VQB3kdOK → hSB1mdM8 → lZS5iMF4 → hdK5iUB8 → dZS9eMFC → VRK5iUNK → dBA3kedC → hUSQNMK8 → ZA62lieG → jcUIVKC6 → dQD9ebOC → VRO1mQNK → lB41mkd4 → lhgRM874 → haY4jGE8 → fZMHWSFA → VKF5iZUK → dKB9edUC → VSR9eNMK → VB63kidK → hcSAdMC8 → ZTQ5iOLG → dJ81mgVC → lYRBcNG4 → hRI3kWN8 → hZE3kaF8 → hZMJUSF8 → ZKB5idUG → dSJ9eVMC → VRC5icNK → dQB3kdOC → hSR1mNM8 → lZ63kiF4 → igcJUC87 → bYQAdOGE → TNI1mWRM → lE73kha4 → igaLSE87 → bYM6hSGE → bNI5iWRE → dNE3kaRC → hRM3kSN8 → hZ63kiF8 → hcZJUFC8 → ZQKAdUOG → TJA1meVM → lUC6hcK4 → hbQ9eOD8 → ZVO1mQJG → lJC1mcV4 → lhQBcO74 → haR1mNE8 → lZM3kSF4 → igK5iU87 → dbY9eGDC → VROHWQNK → FB41mkda → lgSKTM84 → hY95ifG8 → dZWHWIFC → RKFDaZUO → NKA2leUS → jUA4jeK6 → fdU9eKBA → WUS9eMKJ → VDA5iebK → dUOAdQKC → TRA1meNM → lU73khK4 → iga9eE87 → bYVLSJGE → NIC6hcWS → bQE4jaOE → fNM1mSRA → lV63kiJ4 → igcBcC87 → bYRPONGE → NI40nkWS → ngE4ja82 → lfYLSG94 → hWI6hWI8 → bZEDaaFE → OMMJUSSR → B662liie → jccSLCC6 → dQQ6hOOC → bR21mmNE → lkN3kR44 → igg3k887 → hbYXGGD8 → ZOIGXWQG → JHE1maXW → lMGCbYS4 → hPI5iWP8 → dZDooaFC → cbO0nQDD → nPO1mQP2 → mk1oom43 → nli1m632 → mkibC643 → jgcOPC86 → dYQ0nOGC → nRI1mWN2 → mkE3ka43 → jhgLS876 → daY6hGEC → bRMHWSNE → NF63kiZS → hcK4jUC8 → fZQ9eOFA → WUK1mUKJ → lDA9eeb4 → hVUNQKJ8 → ZCA2lecG → jUQIVOK6 → dDA1mebC → lURNQNK4 → hA42lke8 → jgZTKF86 → dYK8fUGC → XRI9eWNI → VFE3kaZK → hMKAdUS8 → ZTA5ieLG → dUJ7gVKC → ZRC9ecNG → VQJ3kVOK → hCB1mdc8
947 max steps4000000Pn → nP3oookP2 → mlPNoQP33 → ljO0onQ54 → ojgKoT851 → njbLoSD52 → miWFoYI63 → lgTFoYL84 → kdRCobNB5 → jZRDoaNF6 → iWLBocTI7 → hXKAodUH8 → gXMCobSH9 → fUKAodUKA → eVJ9oeVJB → fTLBocTLA → eUH7ogXKB → hVNCobRJ8 → gVI7ogWJ9 → hXOCobQH8 → gVK8ofUJ9 → gXMAodSH9 → fWMAodSIA → eVL9oeTJB → fTL9oeTLA → fVJ7ogVJA → hWMBocSI8 → gWK9oeUI9 → fXMBocSHA → eULAodTKB → eTJ8ofVLB → gUL9oeTK9 → fXK8ofUHA → gVOCobQJ9 → fUI6ohWKA → iXNBocRH7 → hXL9oeTH8 → gYNBocRG9 → fVMAodSJA → eVK8ofUJB → gULAodTK9 → fWJ8ofVIA → gVNCobRJ9 → fUI7ogWKA → hWNBocRI8 → gWK8ofUI9 → gXNBocRH9 → fVL9oeTJA