What is the N:th number which, when raised to an odd power, always ends with the same number?

For example, 49^k always ends with 49 for all odd k. Same with 76, for example 76^5 = 2535525376. Some of the first numbers that have this property are 1, 25, 49, 51, 76, 99, etc.

Is there a way to determine the N:th number?