A096550 Consecutive internal states of the IMSL pseudo-random number generator RNUN when started with ISEED=1.

1, 16807, 282475249, 1622650073, 984943658, 1144108930, 470211272, 101027544, 1457850878, 1458777923, 2007237709, 823564440, 1115438165, 1784484492, 74243042, 114807987, 1137522503, 1441282327, 16531729, 823378840, 143542612, 896544303, 1474833169, 1264817709, 1998097157

Offset: 1

Author

Hugo Pfoertner, Jul 18 2004

Keywords

• nonn
• easy

Comments

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 analyzed by Lewis, Goodman and Miller (see link).

Also used by Lotus 1-2-3 and some versions of APL. - Sean A. Irvine, May 27 2025

References

• 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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Eric M. Schmidt)
• D. Y. Downham and F. D. K. Roberts, Multiplicative congruential pseudo-random number generators. The Computer Journal, Volume 10, Issue 1, 74-77.
• George S. Fishman and Louis R. Moore, A Statistical Evaluation of Multiplicative Congruential Random Number Generators with Modulus 2^31-1, J. American Statistical Assoc., 77, 377 (1982), 129-136.
• Pierre L'Ecuyer, Efficient and portable combined random number generators, C ACM, 31, 6 (1988), 742-749 and 774.
• 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.
• 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), 1192-1201.
• B. D. Ripley, Computer Generation of Random Variables: A Tutorial, International Statistical Review, 51 (1983), 301-309.
• B. D. Ripley, Thoughts on pseudorandom number generators, J of Computational and Applied Mathematics, 31, 1 (1990), 153-163.
• Index entries for sequences related to pseudo-random numbers.

Crossrefs

Cf. A096551-A096561 (other pseudo-random number generators); A061364, A384406.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(16807 *a(n-1), 2147483647))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 10 2014

Mathematica

NestList[Mod[#*16807, 2^31 - 1] &, 1, 50] (* Paolo Xausa, Aug 29 2024 *)

PARI

A096550(n)=lift(Mod(16807,1<<31-1)^(n-1)) \\ M. F. Hasler, May 14 2015

Formula

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