Serhiy Storchaka <[email protected]> added the comment:
Here is more optimized PR inspired by PR 29020. It would be too long to explain
how PR 29020 can be improved, so I write a new PR.
Basically it implements Raymond's idea #1, but supports n>62 for smaller k.
How to calculate limits:
import math
n = m = 2**64
k = 1
while True:
nmax = int(math.ceil((m * math.factorial(k-1)) ** (1/k) + (k-1)/2)) + 100
n = min(n, nmax)
while math.comb(n, k) * k >= m:
n -= 1
if n < 2*k: break
print(k, n)
k += 1
----------
versions: +Python 3.11 -Python 3.8, Python 3.9
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