Base 41: 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
23 max steps10 → 0e → d1 → b3
321 max steps100 → 0ee → de1 → ce2 → be3 → ae4 → Ze5 → Ye6 → Xe7 → We8 → Ve9 → UeA → TeB → SeC → ReD → QeE → PeF → OeG → NeH → MeI → LeJ → KeK
44 max stepsL000 → KeeK → KJKL → 1eed → d0d2
519 max stepsJ0000 → IeeeM → MHeMJ → N2ebI → cIeL3 → bJeK4 → aHeM5 → ZIeL6 → YGeN7 → XHeM8 → WFeO9 → VGeNA → UEePB → TFeOC → SDeQD → REePE → QCeRF → SBeSD → TEePC → SEePD
661 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 → B93aVU
730 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 → UL9eUJB
854 max steps5000059a → a954ZZV5 → WUULIAA9 → NKK2bKKI → Z4eeeeZ6 → aY54ZZ65 → WUURCAA9 → NKKEPKKI → B4eeeeZU → aTA4ZUB5 → WUKHMKA9 → NK4eeZKI → aMF2bPI5 → ZVA3aU96 → XTMJKIB8 → PI40daMG → dW93aV82 → bXOLIG74 → XQ82bWE8 → ZPOBSGF6 → THA7WUNC → PKH5YNKG → T95eeYVC → ZVM1cI96 → bTM3aIB4 → YWI3aM87 → XRO3aGD8 → XPE7WQF8 → QOC9USGF → LGB7WTOK → PI80dWMG → dO93aVG2 → bXM7WI74 → XQP3aFE8 → XPC9USF8 → PLG9UOJG → L981cWVK → bOM0dIG4 → dX83aW72 → bXQNGE74 → XQC6XSE8 → RPGBSOFE → HDA7WURO → PKE6XQKG → RC8eeVSE → WSH0dNC9 → dNG5YOH2 → bT85YWB4 → XTOHMGB8 → PI84ZWMG → VO93aVGA → XML7WJI8 → QO41caGF → bWB7WT84 → XPOHMGF8
944 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 → XPH7eWNF8
10113 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 → XQPO3aGFE8