Base 47: 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
26 max steps10 → 0k → j1 → h3 → d7 → VF → FV
324 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 → NkN
44 max stepsO000 → NkkN → NMNO → 1kkj → j0j2
521 max stepsM0000 → LkkkP → PKkPM → Q2khL → iLkO3 → hMkN4 → gKkP5 → fLkO6 → eJkQ7 → dKkP8 → cIkR9 → bJkQA → aHkSB → ZIkRC → YGkTD → XHkSE → WFkUF → VGkTG → UEkVH → WDkWF → XGkTE → WGkTF
686 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 → dP1iL8
736 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 → aNDkWNB
895 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 → hZA7caB4
953 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 → cTI7kcSH9