import math


def spiraldistance(pos):
    if pos == 1:
        return 0
    prev = int(math.sqrt(pos))
    if prev % 2 == 0:
        prev -= 1
    sidelength = prev + 1
    offset = (pos - (prev**2)) % sidelength
    middle = sidelength // 2
    return middle + abs(middle - offset)


tests = {1: 0, 12: 3, 23: 2, 1024: 31}
for pos, expected in tests.items():
    assert (
        spiraldistance(pos) == expected
    ), f"spiraldistance({pos}) => {spiraldistance(pos)}, not {expected}"

spiraldistance(inputvalue)

from itertools import count, cycle, islice, product


def summed_larger():
    grid = {(0, 0): 1}
    directions = tuple((x, y) for x, y in product((-1, 0, 1), repeat=2) if x or y)
    steps = cycle([(0, 1), (-1, 0), (0, -1), (1, 0)])
    step = next(steps)
    x, y = 1, 0
    size = 3
    yield 1
    for num in count(2):
        value = sum(grid.get((x + dx, y + dy), 0) for dx, dy in directions)
        yield value
        grid[(x, y)] = value
        if num == size**2:  # next spiral ring
            size += 2
            x += 1
            step = next(steps)
        else:
            if (num - ((size - 2) ** 2)) % (size - 1) == 0:  # change direction
                step = next(steps)
            x += step[0]
            y += step[1]


print(list(islice(summed_larger(), 25)))
next(filter(lambda v: v > inputvalue, summed_larger()))