A096551 -id:A096551 - cp's OEIS frontend

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

Hugo Pfoertner, Jul 18 2004

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

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.

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.

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

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

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

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

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

A096552 Consecutive internal states of the linear congruential pseudo-random number generator MTH$RANDOM that is used in the VAX VMS Library.

Original entry on oeis.org

0, 1, 69070, 475628535, 3277404108, 772999773, 3877832058, 3821835443, 1662200408, 2044158073, 3788989926, 797919023, 2743624612, 1156259413, 1059494674, 584849259, 786050992, 3369345009, 3077427454, 1200308583, 2654771836, 1692139853, 4052415402, 1850655011

Offset: 1

Hugo Pfoertner, Jul 18 2004

nonn

This generator is a variant of A096551.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
George S. Fishman, Multiplicative Congruential Random Number Generators with Modulus 2^beta: An Exhaustive Analysis for beta = 32 and a Partial Analysis for beta = 48, Math. Comp., 54, 189 (1990), 331-344.
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.

Cf. A096550-A096561 for other pseudo-random number generators.

a:= proc(n) option remember; `if`(n<2, 0,
      irem(69069 *a(n-1)+1, 4294967296))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 10 2014

NestList[Mod[#*69069 + 1, 2^32] &, 0, 50] (* Paolo Xausa, Aug 29 2024 *)

a(1)=0, a(n) = (69069*a(n-1)+1) mod 2^32. The sequence is periodic with period length 2^32. [Corrected based on a comment from Kevin Ryde, Nov 13 2024]

A384933 Consecutive states of the linear congruential pseudo-random number generator (1589013525*s + 1) mod 2^32 when started at s=1.

Original entry on oeis.org

1, 1589013526, 2788435407, 2237951484, 147543469, 4023452466, 2064276251, 628809016, 3191326105, 3400909198, 226805927, 423946676, 1664555973, 2001363754, 382458483, 1721986928, 3087754289, 537519110, 491142271, 2895284844, 187886301, 2237693986, 992271051

Offset: 1

Sean A. Irvine, Jun 12 2025

Periodic with period 2^32.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
B. D. Ripley, Computer Generation of Random Variables: A Tutorial, International Statistical Review, 51 (1983), 301-309.
Index entries for sequences related to pseudo-random numbers.

Cf. A096551-A096561 (other pseudo-random number generators).

NestList[Mod[1589013525*# + 1, 2^32] &, 1, 30] (* Paolo Xausa, Jun 13 2025 *)

a(n) = (1589013525*a(n-1) + 1) mod 2^32.

cp's OEIS Frontend

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

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A096552 Consecutive internal states of the linear congruential pseudo-random number generator MTH$RANDOM that is used in the VAX VMS Library.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A384933 Consecutive states of the linear congruential pseudo-random number generator (1589013525*s + 1) mod 2^32 when started at s=1.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula