The generalized taxicab number T(n,m,t) is equal to the smallest number that is the sum of n positive mth powers in t ways. This definition is inspired by Ramanujan's observation that 1729 = 13+123 = 93+103 is the smallest number that is the sum of two cubes in two ways and thus 1729 = T(2, 3, 2). In this paper we prove that for any given positive integers m and t, there exists a number s such that T(s+k,m,t) = T(s,m,t)+k for every k ≥ 0. The smallest such s is termed the seed for the generalized taxicab number. Furthermore, we find explicit expressions for this seed number when the number of ways t is 2 or 3 and present a conjecture for t ≥ 4 ways.