Trying to Sync weekdays between 2 years - algorithm

Question

I'm trying to come up with something to Sync weekdays between years
So far I can do it for a 4 year gap just by subtracting 364 days
For example
Monday Feb 1 2021 - 364 days becomes Monday Feb 3rd 2020
Friday Feb 19 2021 - 364 days becomes Friday Feb 21nd 2020
Tuesday Mar 2 2021 - 364 days becomes Tuesday Mar 3rd 2020
notice how the weekday is in perfect sync (Monday to Monday, Tuesday to Tuesday etc)
and I can do this for 2 years just by using 728 days (364 * 2)
and so on for 3 and 4 years
my problem is after 4 years it stops working
if I do the same thing for 5 Years (364*5)
Monday Feb 1st 2021 becomes Monday Feb 8th 2016
however I would want it to be Monday Feb 1st 2016
I cant seem to crack how to deal with this for 5 years on

Answer 1

This is using Zeller’s Rule to get the day number, and then just modifying the actual date when subtracting 365 days to get the day name to match. I'm sure there are edge cases (e.g. I believe this would currently allow a result of something like "March 33"), but this should get you started:
const days = ['Sun', 'Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat']
const months = ["January", "February", "March", "April", "May", "June",
"July", "August", "September", "October", "November", "December"
];
const dayNum = (day, month, year) => {
if (month <= 2) {
year--;
month += 12;
}
month-=2;
const lastTwoDigitsOfYear = year % 100;
const firstTwoDigitsOfYear = (year - lastTwoDigitsOfYear) / 100
let F = day + Math.floor((13*month-1)/5) + lastTwoDigitsOfYear + Math.floor(lastTwoDigitsOfYear/4) +Math.floor(firstTwoDigitsOfYear/4)-2*firstTwoDigitsOfYear
let f = F >= 0 ? (F % 7) : 7 + (F % 7);
return f
}
// Ok, so we can get the day for any date.
const syncedYearAdd = (day, month, year, numYears) => {
const d1 = dayNum(day, month, year);
const d2 = dayNum(day, month, year + numYears);
if (d1 < d2) {
day -= (d2 - d1)
} else if (d1 > d2) {
day += (d1 - d2);
}
if (day < 0) {
day += 7;
}
console.log(days[d1], day, months[month-1], year + numYears)
}
// Monday Feb 1st 2021
for (let i = 0; i <= 5; i++) {
syncedYearAdd(1, 2, 2021, i * -1)
}