A fast spigot algorithm for the digits of Tau.

tauG3.py

"""
This algorithm is based on an unproven conjecture but successfully produces at least the first 600 thousand digits.
Read more about it here: https://www.gavalas.dev/blog/spigot-algorithms-for-pi-in-python/
"""

def gospers_tau_unproven():
    q,r,t,i = 1, 180, 30, 2
    while True:
        u,y = 3*(3*i+1)*(3*i+2), (q*(27*i-12)+5*r)//(5*t)
        yield y
        q,r,t,i = 10*q*i*(2*i-1),10*u*(q*(5*i-2)+r-y*t),t*u,i+1
        
        
tau = gospers_tau_unproven()
print([next(tau) for _ in range(10)])