Formulating the randomness for a 512 bits binary number

My data will have 512 bits in binary (1s and 0s) and it can be any combination of the super set - 2^512. For a given data of 512 bits, I would like to understand where and all 1s is present and represent the same using a formula so that I can regenerate the original data using the formula later. Could someone help me if there is any easier way to do the same?

Ex: Assume that my data is a repeat of 1s and 0s - 101010101010.....until it reaches 512 bits. So the formula will be something like 2X, where X=1 through 256.

I looked at the below WIKI - but couldnt understand it fully. http://oeis.org/

I need this info urgently and your immediate help would be highly appreciated.