Infinitely many math beasts stand in a line, all six feet apart, wearing masks, and with clean hands.

Since Grogg is generous, he decides to give away his n pieces of candy. He gives one piece of candy to each of the next n beasts in line and then leaves the line.

The other beasts repeat this process: the beast in the front, who has k pieces of candy, passes one piece each to the next k beasts in line and then leaves the line.

For some values of n, another beast (besides Grogg) temporarily holds all the candy. For which values of n does this occur?

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