The square root of 2 is 1.41421356237 … Multiply this successively by 1, by 2, by 3, and so on, writing down each result without its fractional part:

two-timing 1

Beneath this, make a list of the numbers that are missing from the first sequence:

two-timing 2

The difference between the upper and lower numbers in these pairs is 2, 4, 6, 8 …

From Roland Sprague, Recreations in Mathematics, 1963.