This paper is concerned with the gap test for random sequences, first proposed by Kendall and Babington-Smith , and with various extensions to this test. One of these extensions is the test proposed by Meyer, Gephart and Rasmussen , another is, asymptotically, a partitioning of the $\chi^2$ statistic of Kendall and Babington-Smith , and others are likelihood ratio tests based on Markov chain models.
"The Gap Test for Random Sequences." Ann. Math. Statist. 32 (2) 524 - 534, June, 1961. https://doi.org/10.1214/aoms/1177705058