3 ms·
On infinite decimal expansions, missing numbers, and generating functions (2021)
- dataflow 5y agoAlso see generatingfunctionology: https://www2.math.upenn.edu/~wilf/DownldGF.html https://www2.math.upenn.edu/~wilf/DownldGF.html
- svat 5y agoGreat stuff. The incredible identity at the end checks out: import sympy def divisor_power_sum(n, k): return sum(d**k for d in sympy.divisors(n)) n = 0 while True: n += 1 lhs = divisor_power_sum(n, 7) rhs = divisor_power_sum(n, 3) + 120 * sum( divisor_power_sum(m, 3) * divisor_power_sum(n - m, 3) for m in range(1, n)) print(n, lhs, rhs) assert lhs == rhs (Yes I see sympy has a `divisor_sigma` already, but I wanted to implement it myself.) (BTW, one of my earliest well-received comments on HN, back from 2015, was about 1/999999999999999999999998999999999999999999999999, discussed in the post: https://news.ycombinator.com/item?id=9816375 https://news.ycombinator.com/item?id=9816375)