1,2

This generator is also called "The minimal standard generator" or LCG16807 by L'Ecuyer. Generators of this form are ascribed to D. H. Lehmer, first described by Hutchinson and independently by Downham and Roberts (see link). It was first analysed by Lewis, Goodman and Miller (see link).

D. W. Hutchinson, A new uniform pseudo-random number generator. Comm, ACM 9, No. 6, 432-433, 1966.

D. E. Knuth, The Art of Computer Programming Third Edition. Vol. 2 Seminumerical Algorithms. Chapter 3.3.4 The Spectral Test, Page 108. Addison-Wesley 1997.

Stephen K. Park and Keith. W. Miller: Random Number Generators: Good Ones are Hard to Find, Communications of the ACM, Volume 31, Number 10 (October, 1988), pp. 1192-1201

D. Y. Downham and F. D. K. Roberts, Multiplicative congruential pseudo-random number generators. The Computer Journal, Volume 10, Issue 1, pp. 74-77

Pierre L'Ecuyer, Software for Uniform Random Number Generation: Distinguishing the Good and the Bad. Proceedings of the 2001 Winter Simulation Conference, IEEE Press, Dec. 2001, 95-105

P. A. W. Lewis, A. S. Goodman, and J. M. Miller, A pseudo-random number generator for the System/360, IBM Systems Journal, Volume 8 Issue 2, 136-146, 1969

a(1)=1, a(n) = 7^5 * a(n-1) mod (2^31-1). The sequence is periodic with period length 2^31-2.

Cf. A096551 - A096561 for other pseudo-random number generators.

Sequence in context: A017357 A017477 A017609 this_sequence A061364 A088164 A035922

Adjacent sequences: A096547 A096548 A096549 this_sequence A096551 A096552 A096553

nonn

Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 18 2004