I try to discover the formula behind a video game system. My goal is to create a tool that will help players. The bonus granted by this system follows a logarithmic curve whose values are integers :
$0,3,4,5,6,7,8,8,9,9,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,17,17,...$
$Floor(log(X)10)$, where $X$ is the index of the value in the series, gives good results without being perfect either :
$0,3,4,5,6,6,7,8,9,9,10,10,10,11,11,11,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,...$
Here are the differences highlighted ( index - expected result - result before floor ) :
- 5 - 7 - 6.989
- 6 - 8 - 7.781
- 16 - 11 - 12.041
- 20 - 12 - 13.01
- 49 - 17 - 16.901
- 50 - 17 - 16.989
What can I change to correct these differences?