Base 44: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
22 max steps20 → 1g → e3
323 max steps100 → 0hh → gh1 → fh2 → eh3 → dh4 → ch5 → bh6 → ah7 → Zh8 → Yh9 → XhA → WhB → VhC → UhD → ThE → ShF → RhG → QhH → PhI → OhJ → NhK → MhL → LhM
410 max steps4007 → 73db → aTD8 → SFRG → DAWV → MHPM → 7hha → a6a8 → URFE → GBVS → KBVO
521 max stepsL0000 → KhhhN → NJhNL → O1hfK → gKhM2 → fLhL3 → eJhN4 → dKhM5 → cIhO6 → bJhN7 → aHhP8 → ZIhO9 → YGhQA → XHhPB → WFhRC → VGhQD → UEhSE → TFhRF → SDhTG → UChUE → VFhRD → UFhRE
673 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 → cNJNK6
721 max steps800000M → M7hhhZM → aLKhMM8 → ZG0hgR9 → hXIhOA1 → gXEhSA2 → fWIhOB3 → eUDhTD4 → dRGhQG5 → cNAhWK6 → bSBhVF7 → aQFhRH8 → ZL9hXM9 → YQBhVHA → XNDhTKB → WK8hYNC → ZMBhVL9 → YO9hXJA → YODhTJA → XL9hXMB → YMBhVLA → XN9hXKB
8306 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 → SNJFROKG
944 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 → aQJ8hYOH8