When using the Babylonian method to generate successive approximations to the square root of an integer, if one starts with the lowest integer as first approximant, the rationals generated all appear in the list of convergents for the continued fraction. Specifically, the approximants will appear on the convergents list in positions 0, 1, 3, 7, 15, ... , , ... For example, the continued fraction expansion for square root of 3 is [1;1,2,1,2,1,2,1,2...]. Comparing the convergents with the approximants derived from the Babylonian method: