Vlogger

from datetime import date, timedelta

DAYS_IN_YEAR = 365
DAYS_IN_CYCLE = DAYS_IN_YEAR * 4 + 1
LEAP_DAY = 59 # Feb 29th
CYCLE_START = date(2024, 1, 1)

def valid(interval, startDay):

    currentDay = startDay
    VloggedDay = [False] * DAYS_IN_YEAR
    VloggedLeapDay = False

    for _ in range(DAYS_IN_YEAR + 1):
        if currentDay < LEAP_DAY:
            VloggedDay[currentDay % DAYS_IN_YEAR] = True
        elif currentDay > LEAP_DAY:
            VloggedDay[(currentDay - 1) % DAYS_IN_YEAR] = True
        else:
            VloggedLeapDay = True

        currentDay += interval
        currentDay %= DAYS_IN_CYCLE

    return all(VloggedDay) and VloggedLeapDay

for interval in range(2, 45 + 1):
    for startDay in range(DAYS_IN_CYCLE):
        if valid(interval, startDay):
            print(f"{interval:>2}", CYCLE_START + timedelta(days=startDay))

# Output:
#
#  2 2024-02-29
#  2 2026-03-01
#  3 2024-02-29
#  3 2025-03-01
#  4 2024-02-29
#  4 2024-03-01
# 20 2024-02-29
# 20 2024-03-01
# 20 2024-03-02
# 20 2024-03-03
# 20 2024-03-04
# 20 2024-03-05
# 34 2025-03-01
# 34 2025-03-02
# 34 2025-03-03
# 34 2025-03-04
# 34 2025-03-05
# 34 2025-03-06
# 34 2025-03-07
# 34 2025-03-08