Prague clocks (Q316834)

The Prague clock is a periodic sequence of natural numbers into which plus signs can be inserted to make such sums that form the positive integers in their natural order. For example, the clock in the old square in Prague strikes the hours in the following way: take the periodic sequence (123432) and insert commas and plus signs to get \(1, 2, 3, 4, 3+2, 1+2+3, 4+3, 2+1+2+3, 4+3+2, 1+2+3+4, \dots\), where \(3+2\) means that the clock strikes 5 as bong bong bong pause bong bong. The Prague clock problem is to find all Prague clocks. The paper under review proposes its solution.