It is possible to produce a formula so that any number of your choice could be the next number. Using Occam's razor though, the simplest answer is 54.
The next two numbers after 52,817 would be 52,818 and 52,819. When counting sequentially, each subsequent number increases by 1 from the previous number. Therefore, after 52,817, the next number is 52,818, and the number after that is 52,819.
52 Saturdays and 53 Sundays.52 Saturdays and 53 Sundays.52 Saturdays and 53 Sundays.52 Saturdays and 53 Sundays.52 Saturdays and 53 Sundays.52 Saturdays and 53 Sundays.52 Saturdays and 53 Sundays.52 Saturdays and 53 Sundays.52 Saturdays and 53 Sundays.52 Saturdays and 53 Sundays.52 Saturdays and 53 Sundays.
212.
There were 53 Sundays and 52 Saturdays in 2012.There were 53 Sundays and 52 Saturdays in 2012.There were 53 Sundays and 52 Saturdays in 2012.There were 53 Sundays and 52 Saturdays in 2012.There were 53 Sundays and 52 Saturdays in 2012.There were 53 Sundays and 52 Saturdays in 2012.There were 53 Sundays and 52 Saturdays in 2012.There were 53 Sundays and 52 Saturdays in 2012.There were 53 Sundays and 52 Saturdays in 2012.There were 53 Sundays and 52 Saturdays in 2012.There were 53 Sundays and 52 Saturdays in 2012.
240
The next number would be 212, because the pattern is add 1 (2->3) and times by 4 (3x4=12)... so 52 add 1 = 53, so 53 x 4 =212.
212
-52 + (-53) = -105
107
212 plus 1, times 4
The pattern is: n = n + 1 n = n * 4 repeat So, 2, 3, 12, 13, 52, 53, 112, 113, 452, 453, ...
The LCM of 4, 26, 52, and 53 is 2756