A finite pseudorandom binary sequence

In a series of papers Mauduit and Sarkozy studied finite pseudorandom seque nces. In particular, in Part I they showed that the Legendre symbol forms a n 'ideally good' pseudorandom sequence. In other parts of the series numero us other binary sequences have been tested for pseudorandomness but neither of them proved to be as 'good' as the Legendre symbol. Here another 'very good' sequence is constructed by using the notion of index.