Base 45: 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 steps10 → 0i → h1 → f3b7TFDVHR9ZPJ5dXBLN1hf3
325 max steps100 → 0ii → hi1 → gi2 → fi3 → ei4 → di5 → ci6 → bi7 → ai8 → Zi9 → YiA → XiB → WiC → ViD → UiE → TiF → SiG → RiH → QiI → PiJ → OiK → NiL → MiMLiNMiM
416 max stepsN000 → MiiM → MLMN → 1iih → h0h2he32fa74bSF8TCVGJCVQJ6bQV6bEVGREHAXSNAXMN0hMh0h2
524 max stepsM0000 → LiiiN → NKiNM → O0ihL → iLiM1 → hMiL2 → gLiM3 → fKiN4 → eKiN5 → dJiO6 → cJiO7 → bIiP8 → aIiP9 → ZHiQA → YHiQB → XGiRC → WGiRD → VFiSE → UFiSF → TEiTG → UCiVF → WFiSD → VGiRE → UEiTFUEiTF
6121 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 → PLHQNK951gdafYQHA4bO8ZK8TR3eHGbD9YV8TPHQJGD95cZWXQIPICL86baOVS2fGEdHBWR6XL9YNCPL1gNKf51gd4fbXA74bUMLE8TG0hSGhDBWV2fLHQN4b91gZ8fTPIF4bE6bU8VTFSFEHECVUSJGAXSQNC6bWMVK0hOEhH3eR2fb9Y74bUOJE8TG4dSGZDBWVAPLHQNK
735 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 → XNAiXLCYLBiWNBXNAiXLC
8165 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 → TOD1gVKGfID3eVQ4caI7aQ87VTS7aGFETHEBWURGLGD9YVSOPIC2fWQKdK84daO6ZXS3eGBAbPMBWMJ8TL5iicNGdSH5cRG6YWC9YWCBPNKJOOLK6441geedfaaWB884bSSKNGG8TCC2fWWGdKKCVOO6XJ43eePCbaL5cN88XTS1gGFCfLEBWUN4bLG1gSN8fTC1gWF4fbKDUO74bUH3eRE8bTG9YSF8TPEBWUJGLGD5cVSOXIC2fWQCdLK7aON6XT41geFCfaLDUN84bSH1gRG8fTC9YWF4bPKDUOJ8TH63ecRGbWD9YVC8TPKHQOJGD963ecZWbWQIPIC8TK86baOGVSD3eVGEbIHBWRQ8TLA7aYNGTOD1gVKG
970 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 → aRI7iaQH9bRJ8iZPH8aTI7iaQF9bRLAiXNH8aRG5icSH9dTKAiXOF6cTI8iZQF7bUKAiXOE8aRJ9iYPH9ZRH7iaRHAbQI9iYQI8aSG7iaSG9bRKBiWOH8aQF6ibTI9cSLAiXNG7bSH6ibRG8cTLAiXNF7bSI7iaQG8bTK9iYOF8aSJ8iZPG9aRJ8iZPH9aRI7iaQH9