GEB page 73 sequence

73.py

from bisect import bisect_right

positive = []
negative = []

# https://docs.python.org/3.7/library/bisect.html
def find_gt(a, x):
    'Find leftmost value greater than x'
    i = bisect_right(a, x)
    if i != len(a):
        return a[i]
    raise ValueError

def next_negative():
    last = negative[-1] if negative else 0
    while positive[-1] < last:
        next_positive()
    next = find_gt(positive, last)
    negative.append(last + 1 if last + 1 < next else next + 1)

def next_positive():
    last = positive[-1]
    while len(positive) > len(negative):
        next_negative()
    diff = negative[len(positive)-1]
    positive.append(last + diff)

def run(step):
    positive.clear()
    positive.append(1)
    negative.clear()
    while positive[-1] < 69:
        step()
    print('positive =', positive)
    print('negative =', negative)

print('# next_positive')
run(next_positive)
print()
print('# next_negative')
run(next_negative)