>>11951398you have a * b and you increase a by 1 and decrease b by 1, an increase in a by one leads to an increase of b and a decrease in b by 1 leads to a decrease in a+1, in total when you increase a by 1 and decrease b by 1, you increase the value of a * b by b - (a + 1), look at x - y, for this to be odd x and y cannot be both odd or both even, notice (a+1), this takes a and turns it into an odd number it it were even and vice versa meaning that for b - (a+1) to be odd, b and a must both be either odd or even. this explains why many if not all (i forgot) of the differences shown in your image are odd. (adding 1 to a changes it to either odd or even, subtracting 1 to b changes it to either odd or even, as long as a and b are both odd or both even at the start, the differences of the sequence will always be odd). by looking at the difference, b - (a+1), it is clear why the difference subtracts by two each time, by decreasing b by 1 you decrease the value of b - (a + 1) by 1 and by increasing a by 1 you also decrease the value of b - (a+1) by 1, leading to an overall decrease in the difference of 2
