Base 47: 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
27 max steps10 → 0k → j1 → h3 → d7 → VF → FVFV
326 max steps100 → 0kk → jk1 → ik2 → hk3 → gk4 → fk5 → ek6 → dk7 → ck8 → bk9 → akA → ZkB → YkC → XkD → WkE → VkF → UkG → TkH → SkI → RkJ → QkK → PkL → OkM → NkNMkONkN
427 max stepsO000 → NkkN → NMNO → 1kkj → j0j2jg32hc74dUF8VEVGHEVUHCXULCXQL4fQb4fAbQJAR6dKX6dEXIREJ8bST8bITAZIPAZMP2hMf2h6fYB6ZMNCN0jOj0j2
525 max stepsM0000 → LkkkP → PKkPM → Q2khL → iLkO3 → hMkN4 → gKkP5 → fLkO6 → eJkQ7 → dKkP8 → cIkR9 → bJkQA → aHkSB → ZIkRC → YGkTD → XHkSE → WFkUF → VGkTG → UEkVH → WDkWF → XGkTE → WGkTFVFkUGVEkVGWEkVFWGkTF
695 max stepsF000dd → ddEV78 → WVGTFF → HGCXUU → LECXWQ → LI4fSQ → bA4faA → bRPKJA → R84fcK → bU6dGA → XRDWJE → KI7cSR → VA6daG → XQEVKE → JH5eTS → ZC8bYC → TNLONI → B2kkha → iZ6dB3 → fXNMD6 → ZK0jQC → jN5eN2 → hYkkB4 → gZ8bB5 → bTNMHA → RC0jYK → jM6dO2 → hX1iD4 → hdJQ74 → dW6dE8 → XVHSFE → JGAZUS → PE8bWM → TI2hSI → fB9aZ6 → ZRNMJC → N80jcO → jU0jG2 → jhDW32 → heIR64 → dY8bC8 → VTLOHG → FC2hYW → fMGTO6 → ZD1iXC → hNJQN4 → d6kkd8 → ebkk87 → dc2h88 → fVTGF6 → ZGCXUC → NLDWPO → J40jgS → jc8b82 → hUSHG4 → dEAZW8 → VPHSLG → FB3gZW → dOGTM8 → VD1iXG → hKEVQ4 → dH5eT8 → ZVBYFC → OMFUON → F20jiW → jgGT42 → hcCX84 → dUKPG8 → VE4fWG → bIEVSA → RH9aTK → RC6dYK → XM6dOE → XJ1iRE → hJ7cR4 → dV7cF8 → WUFUGF → HFDWVU → JGCXUS → LE8bWQ → TI4fSI → bB9aZA → SQNMKJ → 960jec → jYSHC2 → hMAZO4 → dP1iL8hV3gF4ecFU87XUEVGEJHDWTSJC8bYSTM8bOITB1iZIhOAZM4dP1iL8
744 max steps90000MN → NM8kbOO → cF0kjV9 → kaMkNA1 → jaDkWA2 → iZMkNB3 → hXCkXD4 → gVJkQF5 → fRBkYJ6 → eUEkVG7 → dQEkVK8 → cPAkZL9 → bSDkWIA → aODkWMB → ZN9kaNC → bOBkYMA → aQBkYKB → ZPDkWLC → YMAkZOD → aMBkYOB → ZPBkYLC → ZNCkXNC → YN9kaND → bNAkZNA → aRBkYJB → ZPEkVLC → YL9kaPD → bNCkXNA → aP9kaLB → bPEkVLA → aN9kaNB → bPCkXLA → aPBkYLB → ZPCkXLC → YNBkYND → ZLAkZPC → aNDkWNBZN8kbNCcPBkYL9bRCkXJAaPDkWLBZNAkZNCaNBkYNBZPAkZLCaNDkWNB
8191 max steps80000Cgg → ggC7cY45 → cbVLOF99 → TSG2hUII → fEB9aZW6 → ZROHSMJC → NB81icZO → hUO0jMG4 → jdE1iW72 → igWHSE43 → fcIAZS86 → ZUP9aLGC → RNE3gWNK → dI6kkdS8 → ecLAZP87 → XUP3gLGE → dJE3gWR8 → dVI7cSF8 → WUG9aUGF → RHEDWWTK → JIC6dYSS → XMA8baOE → TQJ1iRKI → hB85ecZ4 → dZUNMGB8 → VOE0jWMG → jIF1iVS2 → igG9aU43 → fcRDWJ86 → ZUJ7cRGC → VNE7cWNG → VIEkkVSG → WUD2hXGF → fKHDWTQ6 → ZJC5eYRC → ZNM7cONC → VN1kkiNG → jUL7cPG2 → hVE3gWF4 → ecIFUS87 → XUF9aVGE → RJGDWURK → JE86dcWS → XUI8bSGE → TJE9aWRI → RIB7cZSK → VOA6daMG → XQF1iVKE → hJG5eUR4 → dZE7cWB8 → WUOHSMGF → HEB1iZWU → hOICXSM4 → dLA1iaP8 → hVQ3gKF4 → ecG5eU87 → ZXUDWGDC → NKJDWRQO → J860jecS → jYU8bGC2 → hTMDWOH4 → dJC1iYR8 → hVM7cOF4 → dVG1iUF8 → hVGDWUF4 → dJGDWUR8 → VJE7cWRG → VIF7cVSG → VGF9aVUG → RGFDWVUK → JGE6dWUS → XIE8bWSE → TJI9aSRI → RBA7caZK → VQO6dMKG → XF61ieVE → hYJFURC4 → dMF7cVO8 → WUG1iUGF → hHEDWWT4 → dJIBYSR8 → VNA7caNG → VQEkkVKG → WUB4fZGF → bOHDWTMA → RJC1iYRK → hM86dcO4 → dXU1iGD8 → hVKDWQF4 → dJG5eUR8 → ZVE7cWFC → VNIFUSNG → GE9kkaWV → bWK0jQEA → jRI5eSJ2 → 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
955 max stepsB000000CC → CCAkkkZYZ → aYY0kjCCB → kYOLkOMC1 → jYD1kiXC2 → jhWKkPE32 → igTBkYH43 → heVGkTF64 → gbPEkVL95 → fXN9kaND6 → eWN9kaNE7 → dVM8kbOF8 → cVM8kbOF9 → cTM8kbOH9 → cTK6kdQH9 → eUL8kbPG7 → dWL8kbPE8 → cVNAkZNF9 → bSK7kcQIA → dSJ7kcRI8 → dVK8kbQF8 → cVMAkZOF9 → bSK8kbQIA → cRJ7kcRJ9 → dTJ7kcRH8 → dVL9kaPF8 → cUL9kaPG9 → bTK8kbQHA → cRK8kbQJ9 → cTI6kdSH9 → eULAkZPG7 → dUJ8kbRG8 → cVLAkZPF9 → bSK9kaQIA → bRI7kcSJA → dSJ8kbRI8 → cVJ8kbRF9 → cTMBkYOH9 → bRH6kdTJA → eTK9kaQH7 → dVJ8kbRF8 → cVMBkYOF9 → bRJ8kbRJA → cRI7kcSJ9 → dTK8kbQH8 → cVK8kbQF9 → cTMAkZOH9 → bSI6kdSIA → eTJ9kaRH7 → dVJ9kaRF8 → cULBkYPG9 → bRI8kbSJA → cRJ8kbRJ9 → cTI7kcSH9dTLAkZPH8cTI7kcSH9