I have a pattern that I'm struggling to find the formula for.
For inputs of 0 - 3, the expected result is 0.
For inputs 4 - 6, the expected result is 3.
7 - 9 should output 6.
10 - 12 should output 9.
13 - 15 should output 12.
16 - 18 should output 15.
... this pattern repeats ...
0, 1, 2, 3 = 0
4, 5, 6 = 3
7, 8, 9 = 6
10,11,12 = 9
13,14,15 = 12
16,17,18 = 15
...
I'm not as interested in the 0 - 3 part that doesn't "fit the pattern", I can code around that. It's the part of the pattern that repeats that I'm most interested in. How do I "convert" a pattern like this to a "formula"?
Let $\div$ be the integer division operator, then $$a(n)=3\left(\left(n-1\right) \div 3\right)$$ fits the pattern.