A sequence like 1-2-3-4-5-6 will likely never be drawn not because it is a sequential set of numbers but because ANY set of 6 powerball numbers will likely never be drawn.
A random number generator need not be based on "mathematics", ie a formula.
Roulette is a very random process and powerball has orders of magnitude more randomness to it that a single steel ball traveling around a rail on a rotating roulette wheel and no there is no proof that some numbers are more likely than others in roulette despite those who mistakenly try to read some meaning into the past results at a roulette table. You greatly misunderstand the variations that occur in the process of the Powerball picking and how futile it is to even think that using the very small number of games played to detect flaws in the process. Mathematics tells me that too.
Once a roulette ball has been put into motion there IS a mathematical way to determine with better than random chance what set of numbers the ball will end up in. Based on the wheel, the speed of the wheel and the speed of the ball it can be determined approximately at what point on the wheel the ball will fall off the rail. Roulette relies on the variability of the speed of the wheel, release speed and point of the ball AND bans the use of computing devices to determine the more likely sequence of numbers. It also allows players to bet after the three factors have been fixed. The bouncing of the ball on the diamonds and pocket separators are modest but effective randomizers IF the player doesn't have the advantage of a computer and camera to predict where the ball will fall off the rail.
Powerball is substantially different. It uses a shuffling mechanism to randomize the balls along with the variability of the pick time. So once the balls have been shuffling for a few seconds there is no similarity in position, rotational vectors or speeds of the balls. So even if you could take a snapshot of those parameters a few seconds in it would be of no value after a couple more seconds of motion. And Powerball doesn't let you sneak a peek at two seconds into the shuffle and then place a bet.
All of nature involves randomness, at the subatomic level quantum mechanics recognizes that the position of an electronic is only a probability function and quantum objects can pop in and out of existence randomly. Frequency of light is determined entirely by electronics that move from one orbit to another without bothering to actually be anywhere in between those two orbit. Mathematics describes that and mathematics says you can't predict better Powerball numbers either. You really can't.
Finally, since the house edge in Powerball is so enormous, finding a small variable to exploit, such as on ball being slightly smaller or heavier, cannot be used to your advantage. You'll continue to lose and lose a lot. It simply doesn't matter and mathematics tells us that the number of games and number of balls means it is IMPOSSIBLE to detect that advantage by analyzing past draws.
You throw a fair dice 6 billion times and you are almost certain to NOT get exactly 1 billion rolls with each of the 6 numbers showing. And that does not mean the dice are not fair. Powerball is like a 69 sided dice and 26 sided dice that get rolled 100 times a year. It would take tens of thousands of years to detect even a relatively substantial difference in one of the balls that gives it a picking advantage. And, as I said before, it would do you NO GOOD because the house edge is so enormous.
If I have some time I might just do a mathematical analysis that presumes a single ball, lucky #7, has a 10% higher probability of being picked than the other balls. That analysis would tell us how it would affect the house edge, your expected return and also how many draws would have to take place for you to determine to some degree of probability that there is in fact a higher probability of that ball.