  In this survey we summarize properties of pseudorandomness and non-randomness
of some number-theoretic sequences and present results on their behaviour under
the following measures of pseudorandomness: balance, linear complexity,
correlation measure of order $k$, expansion complexity and $2$-adic complexity.
The number-theoretic sequences are the Legendre sequence and the two-prime
generator, the Thue-Morse sequence and its sub-sequence along squares, and the
prime omega sequences for integers and polynomials.
