Base 45: 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 → 0i → h1 → f3
323 max steps100 → 0ii → hi1 → gi2 → fi3 → ei4 → di5 → ci6 → bi7 → ai8 → Zi9 → YiA → XiB → WiC → ViD → UiE → TiF → SiG → RiH → QiI → PiJ → OiK → NiL → MiM
44 max stepsN000 → MiiM → MLMN → 1iih → h0h2
523 max stepsM0000 → LiiiN → NKiNM → O0ihL → iLiM1 → hMiL2 → gLiM3 → fKiN4 → eKiN5 → dJiO6 → cJiO7 → bIiP8 → aIiP9 → ZHiQA → YHiQB → XGiRC → WGiRD → VFiSE → UFiSF → TEiTG → UCiVF → WFiSD → VGiRE → UEiTF
688 max steps3000BL → LB2fXO → dM2fM6 → dWiiB6 → cX6bB7 → WULMED → JG0hSQ → hC6bW2 → fVJOD4 → bI4dQ8 → ZT7aFA → TPDUJG → HD5cVS → XIAXQC → NL7aNM → T20hgG → heCV42 → faIP84 → bS6bG8 → VTBWFE → LHDURO → HA2fYS → dOAXK6 → XN3eLC → bL1gN8 → fT1gF4 → fbDU74 → bUGRE8 → TGAXSG → NDBWVM → LI0hQO → h82fa2 → fdRG54 → bYAXA8 → TOMLKG → D40heW → haIP82 → fS6bG4 → bVBWD8 → TLHQNG → D91gZW → fQIPI4 → b86ba8 → VTRGFE → HEAXUS → NGAXSM → NC0hWM → hK0hO2 → hf3e32 → fca764 → bWSFC8 → TKCVOG → JD3eVQ → bI6bQ8 → VT7aFE → THDURG → HD9YVS → PIAXQK → N84daM → ZS0hGA → hPBWJ2 → fL5cN4 → bX1gB8 → fTLMF4 → bE0hU8 → hTFSF2 → fECVU4 → bJFSP8 → TD5cVG → XICVQC → LJ7aPO → T62fcG → dWCVC6 → XKIPOC → L73ebO → bU2fE8 → dTFSF6 → XECVUC → LJFSPO → D62fcW → dWIPC6 → XK6bOC → VL3eNE → bH1gR8 → fT9YF4 → bPDUJ8 → TH5cRG → XD9YVC → PLHQNK
733 max stepsN000000 → MiiiiiM → MLiiiMN → NMLiMMM → N0iiihM → iMKiNM1 → hO0ihK2 → ifMiL31 → hfJiO32 → geLiM43 → fcIiP64 → eZJiO95 → dVFiSD6 → cQFiSI7 → bN9iYL8 → aSCiVG9 → ZOEiTKA → YL8iZNB → aOCiVK9 → ZOAiXKA → YPCiVJB → XMBiWMC → XL9iYNC → ZMBiWMA → YO9iYKB → ZNDiULA → YM8iZMB → aOBiWK9 → ZPBiWJA → YOCiVKB → XMAiXMC → YLAiXNB → YNBiWLB → XNAiXLC
8119 max stepsM0000Rdd → ddRLMH56 → YXA0hYBB → hONLMLK2 → f420hge4 → hebZ8742 → faUQHE84 → bSG8ZSG8 → TRCBWWHG → LKD9YVOO → PI42feQK → da84da86 → ZXSRGGBA → PMCAXWMK → NK4iidOM → eOH0hRK5 → hZA3eY92 → fbQNKI74 → bU82faE8 → dTSFSGF6 → XEDBWVUC → MKIFSQON → D840heaW → haSIPG82 → fSC6bWG4 → bVKBWOD8 → TLI3eQNG → bD81gaV8 → fTSHQGF4 → bEC8ZWU8 → TRKFSOHG → ECA3eYWV → bOKGROK8 → TB43eeXG → baMCVM88 → TSIiiPGG → SSB2fXGH → dMCAXWM6 → XNJiiOLC → WPC0hWJD → hKJ5cPO2 → fX63ecB4 → caWLMC87 → VSK0hOGE → hHC3eWR2 → fbK9YO74 → bUP3eJE8 → bTG5cSF8 → XTEBWUFC → MKGDUSON → HC40heWS → haKAXO82 → fSN3eLG4 → caC1gW87 → fVSJOGD4 → bIC4dWQ8 → ZTK7aOFA → TPE3eUJG → bGD5cVS8 → XTIBWQFC → MKE7aUON → TG40heSG → haDBWV82 → fSLHQNG4 → bC91gZW8 → fTQJOIF4 → bE84daU8 → ZTSFSGFA → PEDBWVUK → LIG4dSQO → ZC82faWA → dSPJOJG6 → XC64dcWC → ZWLJONCA → PK51gdOK → fY53edA4 → caYNKA87 → VSO2fKGE → dHC3eWR6 → bXK9YOB8 → TPM3eMJG → bD5iicV8 → daP5cJ86 → YWS5cGCB → XNKBWOLC → MK41geON → fa40he84 → hbaRG872 → fUSAXGE4 → bNGBWSL8 → TLC1gWNG → fKD1gVO4 → fbI3eQ74 → caU7aE87 → VTSFSGFE → HEDBWVUS → LIGAXSQO → NC82faWM → dSK0hOG6 → hXC3eWB2 → fbMJOM74 → bU4iidE8 → eaP6bJ85 → ZVS5cGDA → XPIBWQJC → MK85caON → XS40heGC → haLBWN82 → fSL1gNG4 → fbC1gW74 → fbUJOE74 → bUG4dSE8 → ZTGBWSFA → PLEBWUNK → LG51gdSO → fYC2fWA4 → dbOJOK76 → XU53edEC → bYLFSNA8 → TOD1gVKG
949 max steps1000004LM → ML40iheNN → idJ0ihP51 → ihcJiO611 → hhbIiP712 → hfaIiP832 → geXHiQB43 → fcTFiSF64 → eZNDiUL95 → dVM8iZMD6 → cVM8iZMD7 → bUM8iZME8 → aTL7iaNF9 → bRL7iaNH8 → bTJ5icPF8 → dUM9iYME6 → cUK7iaOE7 → bVM9iYMD8 → aSL8iZNG9 → aRJ6ibPH9 → cSJ7iaPG7 → bVK8iZOD8 → aTMAiXMF9 → ZQI6ibQIA → cRH7iaRH7 → bVJ9iYPD8 → aSLBiWNG9 → ZPG6ibSJA → cRJ8iZPH7 → bUI7iaQE8 → bTMBiWMF8 → aQH6ibRI9 → cSJ8iZPG7 → bUJ8iZPE8 → aTLAiXNF9 → ZQI7iaQIA → bQH7iaRI8 → bTJ8iZPF8 → aTK9iYOF9 → ZRJ8iZPHA → aPI7iaQJ9 → bRI6ibQH8 → cTK8iZOF7 → bUK8iZOE8 → aTL9iYNF9 → ZRJ7iaPHA → bQI7iaQI8 → bTI7iaQF8 → bTLAiXNF8 → aRI7iaQH9