Base 41: 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
29 max steps10 → 0e → d1 → b3X7PF9VLJ1db3
323 max steps100 → 0ee → de1 → ce2 → be3 → ae4 → Ze5 → Ye6 → Xe7 → We8 → Ve9 → UeA → TeB → SeC → ReD → QeE → PeF → OeG → NeH → MeI → LeJ → KeKJeLKeK
414 max stepsL000 → KeeK → KJKL → 1eed → d0d2da32bW74XOF8P8VGN8VIN4ZIV4ZAVKJAL0dKd0d2
523 max stepsJ0000 → IeeeM → MHeMJ → N2ebI → cIeL3 → bJeK4 → aHeM5 → ZIeL6 → YGeN7 → XHeM8 → WFeO9 → VGeNA → UEePB → TFeOC → SDeQD → REePE → QCeRF → SBeSD → TEePC → SEePDRDeQERCeRESCeRDSEePD
6138 max stepsB000FK → KFATPL → JA0dUM → dK2bK2 → bYee54 → aZ2b55 → ZVTA96 → TMILIC → H42baO → ZW6X86 → TRNGDC → HE6XQO → RC6XSE → RGCROE → FD7WRQ → PEATQG → JC8VSM → NG2bOI → Z84ZW6 → VTNGBA → LI6XMK → R40daE → dWCR82 → bOEPG4 → XB7WT8 → QOHMGF → B84ZWU → VOILGA → L82bWK → ZO0dG6 → dT7WB2 → bPHMF4 → XA4ZU8 → VPJKFA → LA0dUK → dK0dK2 → daee32 → cb2b33 → aYX665 → VSQDCA → LGCROK → F80dWQ → dOATG2 → bJ7WL4 → XP1cF8 → bP9UF4 → XL9UJ8 → PL1cJG → b91cV4 → bXLI74 → XQ2bE8 → ZPBSF6 → TH9UNC → LH5YNK → T60dYC → dSGNC2 → bG6XO4 → XR7WD8 → QODQGF → DB7WTS → PIEPMG → B93aVUXMILI8P42baGZW8V86TOMHGCH84ZWOVO6XGARL7WJEPD1cRGbE8VQ4XNBSH8PH5YNGT95YVCTMGNICH73aXOXQ6XE8RPBSFEHD9UROLE6XQKRC0dSEdGCRO2bF7WP4XP9UF8PL9UJGL91cVKbM0dI4dX3a72bXPE74XQATE8PJBSLGH91cVObM6XI4XR3aD8XPDQF8PD9URGLE8VQKNC0dSIdG4ZO2bV7W94XPLIF8PA2bUGZK8VK6TMeeHCSN6XHDRF5YPETD9URCLHDQNKD60dYSdSEPC2bGATO4XJ7WL8QO1cGFbB7WT4XPHMF8PA4ZUGVK8VKANKeeJIML2bJJZ31cb6bYSB64XSGNC8PG6XOGR97WVEPMCRIGF93aVQXMATI8PJ3aLGX91cV8bPLIF4XA2bU8ZPJKF6TA0dUCdKGNK2b6eeX4aY3a65XVRC98PMEPIGB93aVU
732 max steps4000000 → 3eeeeeb → b2eeeb4 → ca2eb43 → cZWe753 → bXReC74 → aUKeJA5 → ZQAeTE6 → YPEePF7 → XK9eUK8 → WO9eUG9 → VNDeQHA → UI8eVMB → WKBeSK9 → VL7eWJA → XMBeSI8 → WM9eUI9 → VNBeSHA → UKAeTKB → UJ8eVLB → WKAeTK9 → VM8eVIA → WLCeRJ9 → VK7eWKA → XMAeTI8 → WNAeTH9 → VMBeSIA → UK9eUKB → VJ9eULA → VLAeTJA → UL9eUJBVJAeTLAUL9eUJB
885 max steps300007AI → IA72bXUN → ZQK4ZKE6 → VTBeeSBA → UTK0dKBB → dJHeeML2 → cNK0dKH3 → dZ5eeY52 → cZY0d653 → dZURCA52 → bUKEPKA4 → XKAeeTK8 → WUD8VRA9 → OMKDQKIH → D73eeaXS → bXN4ZH74 → XVQ5YE98 → TPMBSIFC → IGA3aUON → XK84ZWK8 → VPNeeGFA → UPF1cPFB → bJA9UUL4 → XLK1cKJ8 → bP1eecF4 → daNBSH42 → bWH5YN84 → XTO5YGB8 → TPI7WMFC → PHA3aUNG → XK95YVK8 → TPLeeIFC → SPB3aTFD → XIF9UPM8 → PLA3aUJG → XK91cVK8 → bPLeeIF4 → aPJ3aLF5 → XVA1cU98 → bPMJKIF4 → XA40daU8 → dWPJKF82 → bOA0dUG4 → dXK7WK72 → bQOeeFE4 → aQM1cIE5 → bVC3aS94 → YWMFOI87 → RO93aVGE → XMD7WRI8QOE3aQGFXCB7WTS8QOIFOMGFB983aWVUXOMILIG8P842baWGZWO8VG86TON7WHGCPH85YWNGTO95YVGCTMH7WNICPH63aYNGXS95YVC8TPMFOIFCHA93aVUOXMK6XKI8RP3eeaFEbQL1cJE4bXC1cS74bXQFOE74XQC8VSE8PNGBSOHGH985YWVOTOM6XIGCRH83aWNEXOD5YRG8TPE7WQFCPHC9USNGLG95YVOKTM80dWICdOH3aNG2bX85YW74XTQNGEB8PIC6XSMGRG93aVOEXMD7WRI8
945 max stepsF00000QRT → TRQEePEDC → SGDBeSROD → TFFAeTPPC → UHE9eUQNB → VJG8eVOLA → WLF4eZPJ9 → aQH5eYNE5 → ZVK8eVK96 → YRMAeTID7 → XOG8eVOG8 → WPF7eWPF9 → XNH9eUNH8 → WOD5eYRG9 → ZPJAeTLF6 → YPE5eYQF7 → ZRKAeTKD6 → YPG6eXOF7 → YRI8eVMD7 → XQI8eVME8 → WPH7eWNF9 → XNH7eWNH8 → XPF5eYPF8 → ZQI9eUME6 → YQG7eWOE7 → XRI9eUMD8 → WOH8eVNG9 → WNF6eXPH9 → YOH7eWNG7 → XRG6eXOD8 → YPKAeTKF7 → XOE4eZQG8 → aRJ9eULD5 → ZRH7eWND6 → YSJ9eULC7 → XPI8eVMF8 → WPG6eXOF9 → YOH8eVNG7 → XQF6eXPE8 → YPJAeTLF7 → XOE5eYQG8 → ZQJ9eULE6 → YQG6eXOE7 → YRJ9eULD7 → XPH7eWNF8XPH7eWNF8
10156 max steps10000057Hd → dH750dZXN2 → dbUQ5YEA32 → bYTKBSKB64 → XSIGeeNMC8 → WSHA0dUNC9 → dNKG5YOKH2 → bT85eeYWB4 → aZTN2bHB55 → ZVUI5YMA96 → USMK3aKICB → XJG3eeaOL8 → bWKE2bQK84 → ZXOBeeSG76 → YXOH3aNG77 → XRQ85YWED8 → TPOEBSQGFC → IGCA7WUSON → PKG84ZWOKG → VO97eeWVGA → XVMF6XPI98 → RPMA3aUIFE → XKDA3aURK8 → XPKDeeQKF8 → WRI64ZYMD9 → VSNE3aQHCA → XLGC5YSOJ8 → TPG81cWOFC → bOHA7WUNG4 → XPK85YWKF8 → TPO9eeUGFC → VSFD0dRPCA → dLGE9UQOJ2 → bLC81cWSJ4 → bXOG1cOG74 → bXQ87WWE74 → XQPOBSGFE8 → PHCA7WUSNG → PKG95YVOKG → TM97eeWVIC → XVKD6XRK98 → RPMDeeQIFE → RQC82bWSEE → ZOGDBSROG6 → THE87WWQNC → POHC5YSNGG → TG985YWVOC → TOMH7WNIGC → PH863aYWNG → XSO95YVGC8 → TPMG7WOIFC → PHA83aWUNG → XOK95YVKG8 → TPM7eeWIFC → XSHB2bTNC8 → ZPIG5YOMF6 → USA83aWUCB → XOKJFOLKG8 → P981eecWVG → dWTG5YOB82 → bTOI7WMGB4 → XPI83aWMF8 → XPOA3aUGF8 → XPKA7WUKF8 → QOK9eeUKGF → VPE63aYQFA → XSLC9USJC8 → PLGG1cOOJG → b9881cWWV4 → bXOOLIGG74 → XQ882bWWE8 → ZPOOBSGGF6 → THA87WWUNC → POKH5YNKGG → T985eeYWVC → ZWPK1cKF86 → bTO9eeUGB4 → aVQE4ZQE95 → WUMCBSSIA9 → NKHG3aONKI → X864eeZYW8 → aYRQ0dED65 → dVSEBSQC92 → bMHGBSONI4 → XH863aYWN8 → XSPO5YGFC8 → TPGA7WUOFC → PKHA7WUNKG → PK95eeYVKG → ZVIB4ZTM96 → VTMI3aMIBA → XLI43aaMJ8 → XWP41caF88 → bWPO9UGF84 → XOLA7WUJG8 → QOK81cWKGF → bOB7eeWTG4 → aXQG4ZOE75 → WUQC7WSEA9 → PNKGBSOKHG → H985eeYWVO → ZWPF6XPF86 → TROA9UUGDC → LKHE7WQNKK → PC60eedYSG → eYRI2bMD61 → dZSE3aQC52 → bXUGBSOA74 → XQKH7WNKE8 → QOC5eeYSGF → ZSJC1cSLC6 → bTGG1cOOB4 → bXI87WWM74 → XQPO3aGFE8XPCA7WUSF8QOKG9UOKGFLB87eeWWTKXWLC7WSJ88QOOG1cOGGFbB887WWWT4XPOOHMGGF8PA884ZWWUGVOOK8VKGGANL87eeWWJIXWED1cRQ88bPOEBSQGF4XHCA7WUSN8QOKG5YOKGFTB87eeWWTCXWLJeeKJ88WWED0dRQ89dONEBSQHG2bHC85YWSN4XTOG5YOGB8TPI87WWMFCPOHA3aUNGGXK985YWVK8TPOLeeIGFCSPD72bXRFDZQFE9UQPE6TLCC9USSJCLHGG1cOONKb8860dYWW4dXSONGGC72bQG86XWOE4XROC7WSGD8QOGE7WQOGFPCB87WWTSGPOIG8VOMGGN9883aWWVIXOOM4ZIGG8VP883aWWFAXOOL9UJGG8PL881cWWJGbOO91cVGG4bXM87WWI74XQPO3aGFE8