Base 51: 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 steps10 → 0o → n1 → l3 → h7ZFJVBdRN3lh7
328 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 → PoPOoQPoP
412 max stepsQ000 → PooP → POPQ → 1oon → n0n2nk32lg74hYF8ZIVGJCbWPCbQP0nQn0n2
526 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 → YGoXHYGoXH
6139 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 → lZNQF4hK2lU8jZ9eF6dVJUJCRCAdcOTQ2lOMj71mh6ldZEB4hSKTM8Z95ifGdWIVICRECbaOPM2lSQj60ni6ndbCB2lSOPM4h60ni8ncYFC2lQIVO4hD1mb8lZNQF4
746 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 → dPEoZPCcP9oePDfRCobNAeTDoaLBdREoZNCcPBocPDdPCobPCcRBocNDdPEoZPC
8206 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 → hCB1mdc8lZSPOMF4hK60niU8ncZ9eFC2lVQJUOJ4hCB1mdc8
948 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 → fVL9oeTJAfVL9oeTJA