The trouble with enumerating the result - what if it had been 2,000,000,000,000,000,000,000 instead of 20,000?
`2,000,000,000,000,000,000,000 == 2 * 10`^{21} == 5 * 4 * 10^{20} == 5 * (2 * 10^{10})^{2}.
So, all you need to do is list the squares of all numbers from 1 to `sqrt(5) * 2 * 10`^{10}. It'll take a while to list, but you can do it with a one-liner.
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I think the OP was saying "what if the original solutions posted in this thread were used for <insert really large number here> bulbs?". The solutions posted near the top of the thread relied on walking the list numerous times, which is infeasible if the list is super large. The elegance in finding the mathematical property for the bulbs being on is that it *does* scale.
thor
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Feel the white light, the light within`
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