I have a deep lack of interest in big lotteries, so I'm going to answer this in terms of possible strategies people might use to pick a sequence of numbers that are randomly generated.
The first strategy is the familiar one of picking a distinctly systematic sequence such as birthdays, etc. on the mystical belief that since the number is personal, if it is chosen, chance has effectively chosen the chooser and validated them with a prize.
But the second more interesting strategy is that people try to choose a 'random number'. If there is regularity in what they might choose, i.e. if they aren't very good at this, then your 'strategy' would be to choose one of the ones outside these regularities.
There is, it turns out, an interesting line of work assuming that subjective randomness judgements are actually judgements about the representativeness of data from specific generation models, e.g. 'alternation' models of coin flips. Consequently people's judgements of whether a sequence is random are both incorrect and predictable. Some old work that runs with this idea is Griffiths and Tenenbaum (2001) and Griffiths and Tenenbaum (2003). No doubt there is more recent stuff, including lottery-specific things like @chl's JRSS A reference.