def find_integer(f):
    """Finds a (hopefully large) integer such that f(n) is True and f(n + 1) is
    False.

    f(0) is assumed to be True and will not be checked.
    """
    # We first do a linear scan over the small numbers and only start to do
    # anything intelligent if f(4) is true. This is because it's very hard to
    # win big when the result is small. If the result is 0 and we try 2 first
    # then we've done twice as much work as we needed to!
    for i in range(1, 5):
        if not f(i):
            return i - 1

    # We now know that f(4) is true. We want to find some number for which
    # f(n) is *not* true.
    # lo is the largest number for which we know that f(lo) is true.
    lo = 4

    # Exponential probe upwards until we find some value hi such that f(hi)
    # is not true. Subsequently we maintain the invariant that hi is the
    # smallest number for which we know that f(hi) is not true.
    hi = 5
    while f(hi):
        lo = hi
        hi *= 2

    # Now binary search until lo + 1 = hi. At that point we have f(lo) and not
    # f(lo + 1), as desired..
    while lo + 1 < hi:
        mid = (lo + hi) // 2
        if f(mid):
            lo = mid
        else:
            hi = mid
    return lo