Base 44: 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
214 max steps20 → 1g → e3a7SFCVIP6bUDGRAXML0hg1e3
324 max steps100 → 0hh → gh1 → fh2 → eh3 → dh4 → ch5 → bh6 → ah7 → Zh8 → Yh9 → XhA → WhB → VhC → UhD → ThE → ShF → RhG → QhH → PhI → OhJ → NhK → MhL → LhMLhM
415 max steps4007 → 73db → aTD8 → SFRG → DAWV → MHPM → 7hha → a6a8 → URFE → GBVS → KBVOK3dOa3d8aRF8SBVGKBVO
525 max stepsL0000 → KhhhN → NJhNL → O1hfK → gKhM2 → fLhL3 → eJhN4 → dKhM5 → cIhO6 → bJhN7 → aHhP8 → ZIhO9 → YGhQA → XHhPB → WFhRC → VGhQD → UEhSE → TFhRF → SDhTG → UChUE → VFhRD → UFhRETEhSFTDhTFUDhTEUFhRE
6102 max stepsF000KT → TKESNF → FD2eUT → cHDTQ6 → WG8YRC → QKAWNI → M82eZM → cQhhG6 → bRBVG7 → UKAWNE → MG2eRM → cAhhW6 → bX5bA7 → WUMKDC → KH1fQO → e93dY4 → bZOI87 → UR5bGE → WGAWRC → MKAWNM → M2hheM → fLHPM3 → c80gZ6 → gWQGB2 → eL9XM4 → aO0gJ8 → gS4cF2 → eYCU94 → aPHPI8 → S86aZG → URBVGE → KGAWRO → MB3dWM → aKhhM8 → ZNDTK9 → QG2eRI → cB7ZW6 → WSKMFC → KD1fUO → eH3dQ4 → bZ8Y87 → URPHGE → GB7ZWS → SLBVMG → KC0gVO → gJ3dO2 → ea4c74 → aYSE98 → SPDTIG → GC6aVS → UJBVOE → KG4cRO → YB3dWA → aOKMJ8 → S51fcG → eXBVA4 → aNJNK8 → S42edG → cZBV86 → WRJNGC → KB3dWO → aL3dM8 → aS0gF8 → gSCUF2 → eICUP4 → aI6aP8 → US6aFE → UGCURE → IGAWRQ → MB7ZWM → SKhhMG → RN5bKH → WA2eXC → cNJNK6W42edCcZJN86WR3dGCaKAWN8SM2eLGcC0gV6gWIOB2eL5bM4aW0gB8gSKMF2eD1fU4eaGQ74aT9XE8SOESJGEC4cVUYJFROAOC4cVKYJ3dOAaO4cJ8YS4cFAYOCUJAOI4cPKY73daAaTNJE8SF3dSGaDBVU8SKGQNGCA2eXWcNJNK6
740 max steps800000M → M7hhhZM → aLKhMM8 → ZG0hgR9 → hXIhOA1 → gXEhSA2 → fWIhOB3 → eUDhTD4 → dRGhQG5 → cNAhWK6 → bSBhVF7 → aQFhRH8 → ZL9hXM9 → YQBhVHA → XNDhTKB → WK8hYNC → ZMBhVL9 → YO9hXJA → YODhTJA → XL9hXMB → YMBhVLA → XN9hXKBYMChULAXM8hYLBZNBhVK9YOAhWJAXOChUJBWLAhWMCXKAhWNBXMBhVLBWM9hXLCYLAhWMAXOAhWJBXMChULBWL8hYMCZMAhWL9YPAhWIAXODhTJBWK9hXNCYLBhVMAXN9hXKB
8418 max steps100009Ld → dL90gYM5 → gYP0gI92 → geP6aI32 → ebU6aD64 → aVUGQDC8 → SJH9XQOG → OC94cYVK → YPJ3dOIA → aO74caJ8 → YTS4cFEA → YOFCUSJA → OID4cUPK → YH73daQA → aTO8YJE8 → SQF4cSHG → YDC8YVUA → QOJGQOJI → A854ccZY → YXRNJGAA → ONB3dWKK → aL42edM8 → cZS0gF86 → gWRCUGB2 → eLIAWPM4 → aM70gaL8 → gTS0gFE2 → geFCUS32 → ebICUP64 → aVI6aPC8 → USJ6aOFE → UGD4cURE → YHGAWRQA → OMB8YWLK → QL40gdMI → gZ80gZ82 → geRQGG32 → ebB9XW64 → aVOKMJC8 → SJ51fcOG → eXC4cVA4 → aYNIOK98 → SP62ebIG → cVC6aVC6 → WUJIOODC → KH64cbQO → YV93dYCA → aPOIOJI8 → S764cbaG → YVTBVECA → OKJESONK → E542edcU → cZXFRA86 → WRNBVKGC → LJB2eWON → cL51fcM6 → eXW0gBA4 → gaNKMK72 → eT31feE4 → ebaES764 → aVTDTEC8 → SJGESROG → ECB4cWVU → YLJFROMA → OC50gcVK → gXJ3dOA2 → eaN4cK74 → aYT2eE98 → cSPESIF6 → WED6aUTC → UKHESQNE → GE92eYTS → cPFBVSI6 → WKD6aUNC → UKH2eQNE → cG92eYR6 → cWPAWIB6 → WML6aMLC → UK10ggNE → gfG2eR22 → edcAW544 → aZXLLA88 → SRMhhKGG → RR84cZGH → YRB9XWGA → PNLAWMKJ → M630gebM → gbUhhC62 → fbU6aD63 → cVUGQDC6 → WJH9XQOC → OK94cYNK → YP42edIA → cZO6aJ86 → WUR4cGDC → YKHAWQNA → OM92eYLK → cP40gdI6 → gZW6aB82 → eURKMGD4 → aHB1fWQ8 → eSL8YMF4 → aQD0gUH8 → gSH8YQF2 → eQD8YUH4 → aQH8YQH8 → SQ98YYHG → QPC8YVII → QJ86aZOI → UR84cZGE → YRGAWRGA → OMBAWWLK → ML40gdMM → gZ0hhg82 → hfY6a921 → gdUOID42 → eZH5bQ84 → aWR8YGB8 → SQLAWMHG → MC90gYVM → gPIhhOI2 → fPO0gJI3 → gc74ca52 → eYXSEA94 → aPNDTKI8 → SG72eaRG → cTCAWVE6 → WMJESOLC → KE50gcTO → gXF3dSA2 → eaNCUK74 → aTI2ePE8 → cSF6aSF6 → WUDCUUDC → KIHGQQPO → A973daYY → aTPNJIE8 → SF73daSG → aTDBVUE8 → SKHESQNG → EC92eYVU → cPJFROI6 → WC74caVC → YTKIONEA → OF62ebSK → cVD3dUC6 → aWJGQOB8 → SLA4cXMG → YNC0gVKA → gOJ2eOJ2 → ec54cc54 → aYXWAA98 → SPNLLKIG → C72hheaW → faS3dF73 → caTCUE76 → WTIESPEC → KFE6aTSO → UFD3dUSE → aHGCURQ8 → SIB8YWPG → QLC6aVMI → UJ80gZOE → gRG4cRG2 → eYBAWW94 → aPMKMLI8 → S720gfaG → gdTBVE42 → eZKESN84 → aRE2eTG8 → cSFAWSF6 → WMDCUULC → KIH0gQPO → g973daY2 → eaTOIE74 → aTF5bSE8 → WSFCUSFC → KIDCUUPO → IH73daQQ → aT97ZYE8 → TRPESIGF → FDB6aWUT → ULHDTQME → HF90gYSR → gPD9XUI2 → eOH6aQJ4 → aU94cYD8 → YSPGQIFA → ODA6aXUK → UNH3dQKE → aG92eYR8 → cSPAWIF6 → WMD6aULC → UKH0gQNE → gG92eYR2 → ecPAWI54 → aXM6aLA8 → USN0gKFE → gGD2eUR2 → ecHAWQ54 → aXM8YLA8 → SQN0gKHG → gC92eYV2 → ecPIOI54 → aX75baA8 → WTSMKFEC → KFD1fUSO → eHD3dUQ4 → bZH8YQ87 → URQ8YHGE → QGB8YWRI → QLB7ZWMI → SL80gZMG → gRC0gVG2 → geJAWO32 → ebM4cL64 → aYV0gC98 → gSPIOIF2 → eD75baU4 → aWTGQEB8 → SLF9XSMG → ODC0gVUK → gJH3dQO2 → ea94cY74 → aYTOIE98 → SPF5bSIG → WDC6aVUC → UKJGQONE → GA52ecXS → cXNBVKA6 → WNK2eNKC → cK32eeN6 → cbW2eB66 → cWVKMCB6 → WLJ1fOMC → eK50gcN4 → gaX2eA72 → ecTMKE54 → aXF1fSA8 → eSNCUKF4 → aID2eUP8 → cSH6aQF6 → WUD8YUDC → QKHGQQNI → A982eZYY → cRPNJIG6 → WB73daWC → aTLJNME8 → SF40gdSG → gZDBVU82 → eRKGQNG4 → aBA2eXW8 → cSNKMKF6 → WD31feUC → ebKGQN64 → aVA2eXC8 → cSNIOKF6 → WD62ebUC → cVKGQNC6 → WJA2eXOC → cNK4cNK6 → YW32eeBA → cbOKMJ66 → WV51fcCC → eXKIONA4 → aN62ebK8 → cVS2eFC6 → cWJCUOB6 → WLI4cPMC → YK70gaNA → gTO2eJE2 → ecF4cS54 → aYXCUA98 → SPNHPKIG → C872eaZW → cTRJNGE6 → WFB3dWSC → aLKCUNM8 → SI30gePG → gbC6aV62 → eVUIODC4 → aJH5bQO8 → WS94cYFC → YPKCUNIA → OI72eaPK → cT73daE6 → aWTESEB8 → SLFDTSMG → GDC0gVUS → gJHBVQO2 → eK94cYN4 → aYP2eI98 → cSP6aIF6 → WUD6aUDC → UKHGQQNE → GA92eYXS → cPNBVKI6 → WK72eaNC → cTK2eNE6 → cWF2eSB6 → cWLCUMB6 → WLI0gPMC → gK70gaN2 → geT2eE32 → ecbES654 → aXVDTCA8 → SNJFROKGDB52ecWVcXLHPMA6WN80gZKCgRK2eNG2ecB2eW54caXKMA76WTN1fKECeKF2eSN4caD2eU76cWTGQEB6WLF9XSMCOKD0gUNKgH42edQ2ecZ8Y854aXRPHGA8SNB7ZWKGSLC2eVMGcJC0gVO6gWJ4cOB2eYL4cM94aYP0gI98gSP6aIF2eUD6aUD4aUHGQQD8SHA8YXQGQNC8YVKIQJ82eZOIcR84cZG6YWRAWGBAOMLAWMLKM410ggdMgfYhh822ffY6a923dcUOID55YXH5bQAAWON8YKJCQK52ecNIcX82eZA6cWRMKGB6WLB1fWMCeLK0gNM4ga30ge72gebSE632ebVDTC64aVJFROC8SJC4cVOGYJC4cVOAYOJ4cOJAYO54ccJAYXO4cJAAYON4cKJAYO52ecJAcXO4cJA6YWN4cKBAYOL2eMJAcO50gcJ6gXW4cBA2eYNKMK94aP31feI8ebS6aF64aVUCUDC8SJIGQPOGCA74caXWYTNJNKEAOF42edSKcZD3dU86aWRGQGB8SLB9XWMGOLC0gVMKgJ40gdO2geZ4c832ebYQG964aVP9XIC8SOJ6aOJGUC54ccVEYXJFROAAONC4cVKKYJ42edOAcZO4cJ86YWR4cGBAYOLAWMJAOM50gcLKgX40gdA2geZMK832ebR1fG64eaVAWC74aTMIOLE8SF60gbSGgVDBVUC2eKJGQON4aA52ecX8cXSMKFA6WND1fUKCeKH2eQN4ca92eY76cWTOIEB6WLF5bSMCWKD0gUNCgKH2eQN2ec92eY54caXOIA76WTN5bKECWKF2eSNCcKD2eUN6cWH2eQB6cWL8YMB6WQL0gMHCgK90gYN2geP2eI32ecb6a654aXVTDCA8SNJFROKG
967 max steps100000006 → 60hhhhhgc → hb50hgc61 → hgbVhB611 → ggaPhH712 → geZIhO832 → fdWGhQB43 → ebSFhRF64 → dYMChUL95 → cUM8hYLD6 → bUL8hYMD7 → aTL8hYME8 → ZSK7hZNF9 → aQK7hZNH8 → aSI5hbPF8 → cTL9hXME6 → bTJ7hZOE7 → aUL9hXMD8 → ZRK8hYNG9 → ZQI6haPH9 → bRI7hZPG7 → aUJ8hYOD8 → ZSLAhWMF9 → YPH6haQIA → bQH7hZQH7 → aUI8hYPD8 → ZSLBhVMF9 → YOG6haRJA → bQI7hZPH7 → aUI7hZPD8 → aSMBhVLF8 → ZPG6haRI9 → bRJ8hYOG7 → aTI7hZPE8 → aSLAhWMF8 → ZQH6haQH9 → bRI8hYPG7 → aTI8hYPE8 → ZSKAhWNF9 → YPH7hZQIA → aPH7hZQI8 → aSI7hZPF8 → aSK9hXNF8 → ZRI7hZPG9 → aQJ8hYOH8ZSH6haQF9bRKAhWNG7aRG6haRG8bSKAhWNF7aRH7hZQG8aSJ9hXOF8ZRI8hYPG9ZQI8hYPH9ZQH7hZQH9aQI8hYPH8ZSH7hZQF9aQKAhWNH8ZQF5hbSH9cSKAhWNF6bSH7hZQF7aUKAhWND8ZQJ9hXOH9YQG6haRHAbQI9hXPH7aSG7hZRF8aSKBhVNF8ZPG7hZRI9aQJ8hYOH8