N = 1 << 13
Q = [0,1,1] + [0]*(N-2)
for n in range(3, N+1):
    Q[n] = Q[n-Q[n-1]] + Q[n-Q[n-2]]
def e(n): return Q[n] - n/2

# (1) EXACT ERROR LAW: e(n) = e(a)+e(b) - [e(n-1)+e(n-2)]/2 + 3/4 ?
import random
random.seed(1)
worst = 0.0
for _ in range(2000):
    n = random.randrange(10, N)
    a = n - Q[n-1]; b = n - Q[n-2]
    pred = e(a) + e(b) - (e(n-1) + e(n-2))/2 + 0.75
    worst = max(worst, abs(e(n) - pred))
print("(1) exact error law, worst deviation over 2000 random n:", worst)

# (2) THE ASSASSINATION at n=1522: which address hit the spike 768?
print("\n(2) anatomy of the kill:")
for n in range(1518, 1526):
    a = n - Q[n-1]; b = n - Q[n-2]
    hit = " <-- SPIKE" if (a == 768 or b == 768) else ""
    print("  n=%-5d Q=%-5d e=%+7.1f addr=(%d,%d) e_addr=(%+.1f,%+.1f)%s" % (
        n, Q[n], e(n), a, b, e(a), e(b), hit))
print("  spike itself: Q(768)=%d e=%+.1f" % (Q[768], e(768)))

# (3) did ANY k<=8 corridor cell ever address its previous spike?
print("\n(3) spike contact per corridor  [m-64 .. m-1] addressing m_prev:")
for k in range(4, 10):
    m = 3*(1<<k); mprev = m//2
    hits = []
    for n in range(m-64, m):
        a = n - Q[n-1]; b = n - Q[n-2]
        if a == mprev or b == mprev:
            hits.append(n)
    print("  k=%d: corridor cells addressing previous midpoint %d: %s" % (k, mprev, hits[:6]))

# (4) first negative corridor error per generation (the aim slipping left)
print("\n(4) corridor error stats [m-40..m-1]: min e, # negative cells")
for k in range(4, 10):
    m = 3*(1<<k)
    es = [e(n) for n in range(m-40, m)]
    print("  k=%d  min_e=%+.1f  negatives=%d" % (k, min(es), sum(1 for x in es if x < 0)))