merely fiddlin
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For any positive, base-10 integer N, define f(N) as the number of times you have to add up its digits until you get a one-digit number. Find the smallest whole number N such that f(N) = 4. Fiddler on the Proof
Although I first gave in to the R brute force attempt, it failed to return a value for N up to 10⁹, but the solution is obvious as f(N)=p iff F(s(N))=p-1. Since f(19)=2 and f(199)=3, a number N whose sum of digits is 199 is legit, for instance
f(99999999999999999999991)=4
where there are 22 9s. And although it gets a wee bit boring, here is the associated attempt by ChatGPT³
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