Minimum Number of Days to Eat N Oranges

Given n, compute the minimum days to reduce it to 0 when each day you may either eat 1 orange, or—if n is divisible—eat n/2 (leaving n/2) or eat 2*(n/3) (leaving n/3). With n up to 2×10^9 the challenge is to avoid linear DP and use recursion with memoization / divide-and-conquer to explore optimal divide-by-2/3 reductions.