Base 46: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl

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
225 max steps20 → 1i → g3c7UFEVGTCXKP4fa9QJ6dWDIR8bSHAZOL2he5YBMN0ji1g3
325 max steps100 → 0jj → ij1 → hj2 → gj3 → fj4 → ej5 → dj6 → cj7 → bj8 → aj9 → ZjA → YjB → XjC → WjD → VjE → UjF → TjG → SjH → RjI → QjJ → PjK → OjL → NjM → MjNMjN
418 max steps600H → H5dT → YBXC → NKON → 3jjg → g2g4 → eb76 → YTFCMDVOI1hSg9Z4cPJ8U5dGYDVCMHROA1hagPJ4c5d8YTFC
524 max steps10000 → 0jjjj → ijjj1 → i0ji2 → jfj31 → ifj32 → hej43 → gcj64 → fZj95 → eVjD6 → dQjI7 → cKjO8 → bHjR9 → aJjPA → ZGjSB → YIjQC → XFjTD → WHjRE → VEjUF → VFjTF → UFjTG → UDjVGWEjUEVHjRFUDjVG
6224 max stepsA000AN → NA9ZZN → QOjjKK → PP1hKL → g53fe4 → dbYA87 → WTNLGE → ID1hWS → gJ9ZQ4 → cQ6cJ8 → WU6cFE → WIEURE → IG8aTS → SD9ZWI → QJ9ZQK → Q75dcK → YV5dEC → YMGSNC → MC0iXO → iL1hO2 → hf2g43 → fda865 → aXRHCA → QL9ZOK → Q62gdK → eX5dC6 → ZXKOCB → OL3fOM → c31hg8 → gdTF64 → cXDVC8 → ULHROG → EA2gZW → ePHRK6 → YA4eZC → aPLNKA → Q51heK → gZ5dA4 → cYOKB8 → UN3fMG → cE0iV8 → iUGSF2 → gFBXU4 → cMEUN8 → UG0iTG → iECWV2 → gKGSP4 → cC4eX8 → aUKOFA → QF3fUK → cF5dU8 → YUEUFC → MGEUTO → GD1hWU → gJDVQ4 → cI6cR8 → WU8aFE → SIEURI → GA8aZU → SPDVKI → IA4eZS → aP9ZKA → RP4eKJ → a84ebA → aTPJGA → QD5dWK → YJ5dQC → YM6cNC → WM0iNE → iI0iR2 → ig8a32 → gdRH64 → cX9ZC8 → UQKOJG → E73fcW → cVHRE8 → UH9ZSG → QEAYVK → OH5dSM → YB1hYC → gNLNM4 → c20ih8 → ifTF42 → gbDV84 → cTHRG8 → UD9ZWG → QJDVQK → I75dcS → YV9ZEC → QMGSNK → C60idY → iXLNC2 → gL1hO4 → gc2g74 → ecUE76 → YVFTEC → MHDVSO → IB1hYS → gN9ZM4 → cQ0iJ8 → iU6cF2 → gWEUD4 → cJFTQ8 → UE6cVG → WHDVSE → JHAYSR → OB7bYM → UN1hMG → gE0iV4 → icGS72 → gVBXE4 → cMGSN8 → UC0iXG → iLDVO2 → gI2gR4 → ec8a76 → YVRHEC → MH9ZSO → QB1hYK → gN5dM4 → cY0iB8 → iUMMF2 → gEjjU4 → fVBXE5 → aMGSNA → QC0iXK → iL5dO2 → gY2gB4 → ecMM76 → YUjjEC → XV3fED → cKGSP8 → UC4eXG → aLDVOA → QI2gRK → e95da6 → ZXQICB → OL7bOM → U31hgG → gdDV64 → cXHRC8 → UL9ZOG → QE2gVK → eH5dS6 → ZXAYCB → PNKOML → 530igf → idZ962 → gXPJC4 → cL5dO8 → YU2gFC → eMEUN6 → YG0iTC → iMCWN2 → gK0iP4 → ic4e72 → gaUE94 → cRFTI8 → UE8aVG → SHDVSI → IB9ZYS → QN9ZMK → Q60idK → iX5dC2gYKOB4cN3fM8cU0iF8iUEUF2gGEUT4cGCWT8UKCWPGKE4eVQaH5dSAYQAYJCOM6cNMW20ihEifHR42gb9Z84cTPJG8UD5dWGYJDVQCMI6cROW91haEgRHRI4cA8aZ8USOKHGEB3fYWcNHRM8UA0iZGiPDVK2gI4eR4ca8a98USQIHGEB7bYWUNHRMGEA0iZWiPHRK2gA4eZ4caOK98UR3fIGcE8aV8USGSHGECAYXWOLHROMA31hgagdPJ64cX5dC8YUKOFCMF3fUOcF1hU8gUEUF4cGEUT8UGCWTGKECWVQKH5dSQYB5dYCYNLNMCM20ihOif1h42hfa843ebRH86YT9ZGCQMCWNKK60idQiX5dC2
732 max steps800000N → N7jjjbN → cMLjNN8 → bH0jiS9 → jZJjPA1 → iZFjTA2 → hYJjPB3 → gWEjUD4 → fTHjRG5 → ePBjXK6 → dTCjWG7 → cRFjTI8 → bNAjYM9 → aRBjXIA → ZPEjUKB → YL9jZOC → aNCjWMA → ZO9jZLB → aODjVLA → ZN9jZMB → aOCjWLA → ZOAjYLB → ZOCjWLB → YNAjYMC → ZMBjXNB → YOAjYLC → ZMCjWNB → YN9jZMC → aNBjXMAZPAjYKBZODjVLBYM9jZNCaNBjXMA
8404 max steps70000Hff → ffH6cS45 → baWAYD99 → SROIQLII → A982gbaa → eTRPJIG6 → YD95daWC → YRMIQNIC → M980ibaO → iTR1hIG2 → hfD8aW43 → ebSIQH86 → YTB7bYGC → UNMCWNMG → KE10iiVQ → ihH5dS22 → gfYAYB44 → cbOMML88 → UT2jjgGG → hTQ0iJG3 → ieD6cW52 → gZWIQDA4 → cPJ7bQK8 → VT74ecGF → aVGCWTEA → QKHCWSPK → KB64edYQ → aXN5dMCA → YQL0iOJC → iM72gcN2 → geV0iE54 → icZGSA72 → gVPBXKE4 → cMH4eSN8 → aUB0iYFA → iQNEUMJ2 → gG70icT4 → icVCWE72 → gVKGSPE4 → cHC4eXS8 → aULAYOFA → QOF2gULK → eF62gdU6 → eYXEUCB6 → YNLFTOMC → ME30igVO → idH1hS62 → hfXAYC43 → ebOKOL86 → YT42gfGC → ebMCWN86 → YTK0iPGC → iMD4eWN2 → gaJ0iQ94 → icR6cI72 → gWV8aED4 → cSJGSQH8 → UCB6cYXG → WNLDVOME → JH30igSR → idB7bY62 → gXUMMFC4 → cLEjjUO8 → bVH5dSE9 → YSHAYSHC → OMBAYYNM → ON20ihMM → if20ih42 → igfa8432 → gdbRH864 → cXT9ZGC8 → UQLCWOJG → KE72gcVQ → eVH5dSE6 → ZXHAYSCB → PNLAYOML → O430igfM → idb1h862 → hfXSGC43 → ebLBXO86 → YTM2gNGC → eMD0iWN6 → iYJ0iQB2 → igN6cM32 → gdW0iD64 → icXIQC72 → gVL7bOE4 → cUH2gSF8 → eUFAYUF6 → YOFEUULC → MGF2gUTO → eFD1hWU6 → gYJEUQB4 → cNG6cTM8 → WUD0iWFE → iJIEURQ2 → gG96caT4 → cWRCWID8 → UKJ8aQPG → SE74ecVI → aVH9ZSEA → RPHAYSKJ → OB84ebYM → aTN1hMGA → gQD0iWJ4 → icJ6cQ72 → gWV6cED4 → cWJGSQD8 → UJC6cXQG → WLE6cVOE → WIH2gSRE → eIB8aYR6 → YSN8aMHC → SMB0iYNI → iNA0iZM2 → igP0iK32 → igd4e632 → gdaWC964 → cXRJPIC8 → UL95daOG → YRE2gVIC → eMH8aSN6 → YSB0iYHC → iNMAYNM2 → gO10iiL4 → ihc2g722 → gfeUE544 → cbZFTA88 → UTPDVKGG → IED4eWVS → aJH9ZSQA → RPB6cYKJ → WN84ebME → aTI0iRGA → iQD8aWJ2 → gSJ6cQH4 → cWB6cYD8 → WUNIQMFE → IF80ibUS → iTF9ZUG2 → gQFCWUJ4 → cKF6cUP8 → WUF4eUFE → aIFEUURA → QGF8aUTK → SFD5dWUI → YJF9ZUQC → QMF6cUNK → WF60idUE → iXIEURC2 → gLG8aTO4 → cSD2gWH8 → eUJAYQF6 → YOF6cULC → WMF2gUNE → eIF0iUR6 → iYF8aUB2 → gSNEUMH4 → cGB0iYT8 → iUNCWMF2 → gKF0iUP4 → icF4eU72 → gaVEUE94 → cRHFTSI8 → UEB8aYVGSNHDVSMIIBA0iZYSiPN9ZMK2gQ50ieJ4icZ6cA72gWVOKED4cJH3fSQ8cUB6cYF8WUNEUMFEIGF0iUTSiFD9ZWU2gQJEUQJ4cG76ccT8WVUCWFEEKIHEUSRQGB95daYUYRNDVMICMI90iaROiR91haI2hfR8aI43ebS8aH86YTSAYHGCOMDAYWNMOJ20ihQMif71hc42hfbUE843ebTFTG86YTECWVGCMKHCWSPOKB51heYQgZN5dMA4cYP0iKB8iUN4eMF2gaF0iU94icREUI72gVG8aTE4cSHCWSH8UKBAYYPGONE4eVMMaH20ihSAifQAYJ42gbO6cL84cWT2gGD8eUJCWQF6YKF6cUPCWMF4eUNEaIF0iURAiQF8aUJ2gSF6cUH4cWFAYUD8UOJEUQLGGE72gcVUeVHDVSE6YIHAYSRCOMB8aYNMSN20ihMIifA0iZ42igbOK832gdT3fG64dbXCWC87WTLJPOGEID62gdWSeXJ9ZQC6YQL6cOJCWM72gcNEeVI0iRE6iYH8aSB2gSNAYMH4cOB0iYL8iUN2gMF2geF0iU54icZEUA72gVPFTKE4cHE4eVS8aUHAYSFAQOFAYULKOF62gdUMeXF1hUC6gYLEUOB4cNG2gTM8eUD0iWF6iYJEUQB2gNG6cTM4cWD0iWD8iUJIQQF2gF86cbU4cWTEUGD8UJGCWTQGKED6cWVQWJH5dSQEYIB6cYRCWNM8aNMESI10iiRIihA8aZ22gfSOKH44cbB3fY88cUTMMGF8UFCjjWUGXUFjjTFDWUI0iRFEiIF8aUR2gSF8aUH4cSFAYUH8UOFAYULGOFE2gVUMeHF1hUS6gYFAYUB4cONEUML8UG30igTGidECWV62gXKGSPC4cLC4eXO8aUL2gOFAeQF2gUJ6eYF6cUB6YWNEUMDCMJG0iTQOiD71hcW2hfVIQE43ebH7bS86YUTAYGFCOMFCWUNMKF20ihUQifF5dU42gbYEUB84cTNFTMG8UED0iWVGiJHDVSQ2gIB6cYR4cWN8aMD8USJ0iQHGiEB6cYV2gWNGSMD4cJC0iXQ8iUL6cOF2gWF2gUD4ecJEUQ76YVG6cTECWMHCWSNEKIB0iYRQiN95daM2gYR0iIB4icN8aM72gVS0iHE4icHAYS72gVOAYLE4cOH2gSL8eUB2gYF6eYNEUMB6YNG0iTMCiMD0iWN2igJ0iQ32igd6c632gdXVDC64cXLHROC8ULA2gZOGePE2gVK6eYH4eSB6aYNAYMBAQON0iMLKi630igd2igdWC632gdXJPC64cXL5dOC8YUL2gOFCeMF2gUN6eYF0iUB6iYNEUMB2gNG0iTM4icD0iW72igVIQE32gdH7bS64cXUAYFC8UOLEUOLGGE32ggVUedHDVS66YXIAYRCCOML8aONMS320ihgIifd9Z642gbXPJC84cTL5dOG8YUD2gWFCeMJEUQN6YG70icTCiVMCWNE2gKH0iSP4icB4eY72gaVMME94cRGjjSI8bTK0iPG9iSD4eWH2gaJAYQ94cRO6cLI8WU92gaFEeRIEURI6YG98aaTCSRMCWNIIKA90iaZQiRP5dKI2gY94eaB4caRMMI98UR8jjaIGbTI2gRG9eSD8aWH6YSJAYQHCOMB6cYNMWN20ihMEifI0iR42igb8a832gdTRHG64cXD9ZWC8UQLIQOJGE872gcbWeVTHRGE6YHD9ZWSCQMJAYQNKO760idcMiXV1hEC2hfLGSO43ebC2gX86eYTKOGB6YND3fWMCcMJ0iQN8iU70icF2igVEUE32gdHFTS64cXEAYVC8UOLGSOLGEC32ggXWedLHRO66YXA2gZCCePMKONK6Y540ifeCibZLNA82gTP1hKG4gcD4eW74caVIQE98URH7bSIGUEB8aYVG
948 max stepsC00000LMN → NMLBjXONN → YC1jjjhXC → iXX9jZCC2 → hZNKjOMA3 → gXF1jhUC4 → idUHjRF62 → hcOCjWL73 → gaQAjYJ94 → fXQEjUJC5 → eTJAjYQG6 → dUI9jZRF7 → cUKBjXPF8 → bRI9jZRI9 → aSH8jaSHA → bQJAjYQJ9 → aRF6jcUIA → dSLBjXOH7 → cSG6jcTH8 → dUMBjXNF7 → cSI7jbRH8 → cUK9jZPF8 → bTK9jZPG9 → aSJ8jaQHA → bQJ8jaQJ9 → bSH6jcSH9 → dTKAjYPG7 → cTI8jaRG8 → bUKAjYPF9 → aRJ9jZQIA → aQH7jbSJA → cRJ8jaQI8 → bUI7jbRF9 → cSMBjXNH8 → bRG5jdTI9 → eULAjYOF6 → dUJ8jaQF7 → cVLAjYOE8 → bSK9jZPH9 → aSI7jbRHA → cRJ9jZQI8 → bTH7jbSG9 → cSLBjXOH8 → bRG6jcTI9 → dTLAjYOG7 → cTI7jbRG8 → cULAjYOF8 → bSJ8jaQH9bSJ8jaQH9