I made a function to give me the `bitCount`

for an individual number and logged out every number in order until I was able to see the pattern of groups of 4 starting from a number, incrementing 1, repeating, and incrementing 1. Then I noticed that the same pattern occuring over the entire series of numbers occurs for the first of every 4 numbers. Using this knowledge, I decided to keep track of an index that increments ever 4 numbers and gives me that value from the numbers I've already produced in order to determine what number the next group of 4 should start with. Here's what I ended up with. Next steps would be to cache groups of 4 for each starting number so that when I get to a starting number I've been to before, I can just push a copy of them into my array and remove any excess.

```
const countBits = (num) => {
const bitCounts = [0]
let histIdx = 0, val = 0
for (let i = 1; i <= num; ++i) {
if (i % 4 === 0) {
++histIdx
val = bitCounts[histIdx]
}
if (i % 2 === 1) ++val
bitCounts.push(val)
}
return bitCounts
}
```