Geodesic
Periods of Pseudo-Random Sequences
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 2, pp. 367-373

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Sequences of pseudo-random numbers are usually generated by recurrence formulas of the type (1). In order to increase the length $L$ of the non-periodic part of a sequence, the “perturbed” sequence (2) may be used. The asymptotic distributions (3) and (4) of $L$ and $P$ are derived from elementary probability considerations, where $P$ is the length of the period that has been formed. It follows from (5) that in that case one can expect an increase in $L$ and $P$ by the factor $\sqrt M$. A numerical example shows that such distributions may be of practical value, though $P$ can hardly be regarded as random. 
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     author = {I. M. Sobol'},
     title = {Periods of {Pseudo-Random} {Sequences}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a16/}
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I. M. Sobol'. Periods of Pseudo-Random Sequences. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 2, pp. 367-373. http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a16/