A method for generating sequences that approximate binary random sequences with the probability of a 1 equal to 1/4 is described. These are calledPN^2sequences.PN^2sequences are generated by clocking aPNsequence generator at the l's of aPNsequence. ThePN^2sequence is 1 when the generator output makes a transition and is 0 otherwise. It is shown thatPN^2sequences have periodN^2if thePNsequence generators have periodN. The density of l's is shown to approach 1/4 for largeN. It is shown that the normalized out-of-phase pulse-coincidence autocorrelation function can never exceed 1/2 or be less than 1/4 and is 1/4 most of the time for largeN.