Sojourn time test for maximum-length linearly recurring sequences with characteristic primitive trinomials

A new statistical test for random number generators is introduced, which is based on simulations of the arc sine law for sojourn times of 1-dimensional random walks. Results of the tests for maximum-length linearly recurring sequences with characteristic primitive trinomial show statistical biases of those sequences explicitly, when the length of sample paths used in the test is somewhat longer than the degree of the characteristic trinomials.