Problem 50953. Round up to π
To commemorate Pi Day (March 14 in the U.S.), compute the nth term in a sequence by starting with n, rounding up to the next multiple of , rounding up to the next multiple of , and so on to rounding up to the next multiple of 1. For example, with n = 8, you would get 14, 18, 20, 20, 21, 22, and—the element in the sequence— = 22.
Write a function that computes , the nth term in this sequence. Also compute and notice its limit as n gets large. For more on this limit, see this page by K.S. Brown.
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