Base 50: Cycles Sequences: Maximum Length Cycle Count

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 # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
25 cycles8 nodes4j → e9 → UJ → Ad → SL → 6h → aD → MR
31 cycle (fixed) 1 node OnP
48 cycles10 nodesE5ha → cLRC → Q5hO → c1lC → kPN4 → g1l8 → kXF4 → gHV8 → YDZG → MHVS
52 cycles4 nodesXFnXH → YFnXG → YHnVG → XGnWH
610 cycles50 nodesE75hga → cZLREC → QL5hSO → c71lgC → kZPNE4 → gL1lS8 → kY6gF4 → gaIUD8 → YNBbQG → QI2kVO → iD1la6 → kcMQB4 → gR3jM8 → gY4iF8 → eYIUFA → UJBbUK → QB9dcO → UR1lMK → kA4id4 → geSK98 → YV7fIG → YICaVG → OICaVQ → OD1laQ → kN1lQ4 → kg2k74 → igYE76 → cZJTEC → QL9dSO → U71lgK → kZ9dE4 → gUKSJ8 → YB7fcG → YRHVMG → IE4iZW → eLDZSA → UM6gRK → aA4idE → eTLRKA → U95heK → cV9dIC → UQCaNK → OA2kdQ → iT1lK6 → kc8eB4 → gWQMH8 → YF3jYG → gJHVU8 → YEAcZG → SLHVSM
71 cycle 4 nodesbOAncPD → dPCnaOB → cRBnbMC → cQEnYNC
84 cycles349 nodes4320mlkk → mjhf7642 → kfbXFC84 → gXPHVOG8 → YHE0mZWG → mLIEYVS2 → kKD6gaT4 → gaN8eQD8 → YWN2kQHG → iIF2kYV6 → icJCaUB6 → cROAcPMC → SQ50miNM → md62khA2 → kibSKC54 → gdP7fOA8 → ZXT0mKGF → mKH8eWT2 → kWF8eYH4 → gWJEYUH8 → YKFAcYTG → SJI8eVUM → WDB5hcaI → cRNDZQMC → QM52kiRO → id51liA6 → kdcSKBA4 → gTR7fMK8 → ZX94ieGF → eVKGWTIA → UGD8eaXK → WNH9dWQI → UFE2kZYK → iLJ9dUS6 → cUB6gcJC → aRQAcNME → SM52kiRM → id64ihA6 → ecbSKCBA → URP7fOMK → YA50midG → mdTHVKA2 → kTE8eZK4 → gWL8eSH8 → YWF6gYHG → aJIEYVUE → MKDAcaTS → SN95heQM → cV62khIC → ibQCaNC6 → cPO2kPOC → iQ10mmN6 → mlc2kB22 → kjiQM544 → gfd3jA88 → gYXSKGF8 → YJH7fWUG → YIFAcYVG → SJICaVUM → ODB5hcaQ → cRN1lQMC → kQ52kiN4 → igd2kA76 → icZSKEB6 → cRL7fSMC → YQ74igNG → eZI2kVEA → iULCaSJ6 → cOB6gcPC → aRQ0mNME → mM52kiR2 → kid4iA54 → gedSKA98 → YVT7fKIG → YID8eaVG → WNICaVQI → OED2kaZQ → iNL1lSQ6 → kc72kgB4 → igZQME76 → cZL3jSEC → gQL6gSN8 → aY72kgFE → iZMIURE6 → cLC4ibSC → eQP6gONA → aU30mkJE → mhMAcR62 → kbS4iLC4 → geP6gO98 → aYV0mIFE → mMJCaUR2 → kOB4icP4 → geR0mM98 → mYV4iIF2 → keJCaU94 → gVOAcPI8 → YSD0maLG → mNI6gVQ2 → kaD2kaD4 → igNMQQ76 → cZ42kjEC → ifQKSN86 → cX82kfGC → iXQGWNG6 → cHG2kXWC → iQHEYWN6 → cKF2kYTC → iQJ8eUN6 → cWB2kcHC → iRQEYNM6 → cK52kiTC → idQ8eNA6 → cWT2kKHC → iQF8eYN6 → cWJ2kUHC → iQFAcYN6 → cSJ2kULC → iQB6gcN6 → caR2kMDC → iQN4iQN6 → ec32kkBA → ihUQMJ66 → cbB3jcCC → gRQOONM8 → Y52nnkiG → liU9dJ53 → idUAcJA6 → cTSAcLKC → SQ96geNM → aV62khIE → ibMCaRC6 → cPO4iPOC → eQ10mmNA → mlU2kJ22 → kjiAc544 → gfdRLA88 → YXT5hKGG → cIH8eWVC → WQFCaYNI → OJE2kZUQ → iLB1lcS6 → kcR6gMB4 → gaR4iMD8 → eYN4iQFA → eUJ2kUJA → iUBAccJ6 → cSRAcMLC → SQ74igNM → eZ62khEA → ibUKSJC6 → cPB7fcOC → YRQ0mNMG → mI52kiV2 → kidCaA54 → gdTNPKA8 → YT91leKG → kVI8eVI4 → gWDCaaH8 → YONEYQPG → KI30mkVU → mhD9da62 → kbUMQJC4 → gPB3jcO8 → gYR0mMF8 → mYJ4iUF2 → keJAcU94 → gVSAcLI8 → YSD6gaLG → aNI6gVQE → aMD2kaRE → iNM4iRQ6 → ec52kiBA → idUQMJA6 → cTB3jcKC → gRQ8eNM8 → YW52kiHG → idIEYVA6 → cTKCaTKC → QO98eePO → WV20mlII → mjECaZ42 → kfOKSP84 → gX80mfG8 → mYXGWGF2 → kJHFXWU4 → gIFAcYV8 → YSJCaULG → OIB6gcVQ → aRD1laME → kNM4iRQ4 → ge52ki98 → idYUIFA6 → cTJBbUKC → RPB8ecON → WR40mjMI → mfE4iZ82 → keXKSG94 → gVH7fWI8 → ZXFCaYGF → OKJGWUTQ → GB91lecY → kVRHVMI4 → gED4iaZ8 → eYNKSQFA → UJ82kfUK → iXB9dcG6 → cURGWMJC → QGB4icXO → eRH1lWMA → kUF4iYJ4 → geJAcU98 → YVSAcLIG → SID6gaVM → aND5haQE → cNM2kRQC → iQ52kiN6 → idc2kBA6 → icTQMKB6 → cR93jeMC → gVQ4iNI8 → eYD2kaFA → iUNIUQJ6 → cCB2kcbC → iRQOONM6 → c52nnkiC → liY5hF53 → idcIUBA6 → cTRBbMKC → RP94ieON → eV40mjIA → mfUCaJ82 → kXOAcPG4 → gSH0mWL8 → mYF6gYF2 → kaJIUUD4 → gNCAcbQ8 → YSP2kOLG → iI70mgV6 → mcZCaEB2 → kROKSPM4 → g850mif8 → mdYWGFA2 → kTJFXUK4 → gIB8ecV8 → YWRCaMHG → OIF4iYVQ → eJD1laUA → kUNAcQJ4 → gSB2kcL8 → iYR6gMF6 → caJ4iUDC → eQNAcQNA → US32kkLK → ihA6gd66 → cbaSKDCC → QPN7fQOO → Y320mlkG → mjhHV642 → kfbDZC84 → gXPLROG8 → YH60mhWG → mbIEYVC2 → kPKCaTO4 → gO90meP8 → mYV0mIF2 → mkJCaU32 → khOAcP64 → gbS0mLC8 → mYP6gOF2 → kaJ0mUD4 → mgNAcQ72 → kZS2kLE4 → igL6gS76 → caZ6gEDC → aQNKSQNE → M832kkfS → ihX5hG66 → dbbGWCCB → SPPFXOOM → I610mmhW → mlbDZC22 → kjPLRO44 → gf60mh88 → mbYWGFC2 → kPJFXUO4 → gIB0mcV8 → mYRCaMF2 → kOJ4iUP4 → geB0mc98 → mYVQMIF2 → kJD3jaU4 → hfNAcQ87 → aXS2kLGE → iMH6gWR6 → caF4iYDC → eQNIUQNA → UC32kkbK → ihP9dO66 → cbU0mJCC → mQPAcON2 → kS30mkL4 → mhg6g762 → kbaYEDC4 → gPNJTQO8 → YA30mkdG → mhTHVK62 → kbE8eZC4 → gWPKSOH8 → YF80mfYG → mXJHVUG2 → kHEAcZW4 → gSLEYSL8 → YK76ggTG → aZI8eVEE → WMLCaSRI → OE74igZQ → eZL1lSEA → kUL6gSJ4 → gaB6gcD8 → aYRMQMFE → MJ53jiUS → gdB5hcA8 → cYTQMKFC → QJ93jeUO → gVB1lcI8 → kYRCaMF4 → gOJ4iUP8 → eYB0mcFA → mURIUMJ2 → kCB4icb4 → geROOM98 → YV4nniIG → jXQ2kNG5 → ieH2kW96 → icVEYIB6 → cRKCaTMC → QO94iePO → eV20mlIA → mjUCaJ42 → kfOAcP84 → gXS0mLG8 → mYH6gWF2 → kaJEYUD4 → gNKAcTQ8 → YS92keLG → iVI6gVI6 → caDCaaDC → QONMQQPO
96 cycles21 nodesdUJ8neUJB → fTKAncTK9 → eVI8neVIA → fUMCnaRJ9 → eTH7nfWKA → gVNBnbQI8 → fVJ7nfUI9 → gWNBnbQH8 → fVK8neTI9 → fWMAncRH9 → eVL9ndSIA → eUL9ndSJA → eUK8neTJA → fUL9ndSJ9 → eWK8neTHA → fUNBnbQJ9 → eUI6ngVJA → hWMBnbRH7 → gWK9ndTH8 → fXMBnbRG9 → eULAncSJA