cp's OEIS Frontend

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

%I A096550 #57 Jun 22 2025 18:15:02
%S A096550 1,16807,282475249,1622650073,984943658,1144108930,470211272,
%T A096550 101027544,1457850878,1458777923,2007237709,823564440,1115438165,
%U A096550 1784484492,74243042,114807987,1137522503,1441282327,16531729,823378840,143542612,896544303,1474833169,1264817709,1998097157
%N A096550 Consecutive internal states of the IMSL pseudo-random number generator RNUN when started with ISEED=1.
%C A096550 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).
%C A096550 Also used by Lotus 1-2-3 and some versions of APL. - _Sean A. Irvine_, May 27 2025
%D A096550 D. W. Hutchinson, A new uniform pseudo-random number generator. Comm, ACM 9, No. 6, 432-433, 1966.
%D A096550 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.
%H A096550 Alois P. Heinz, <a href="/A096550/b096550.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Eric M. Schmidt)
%H A096550 D. Y. Downham and F. D. K. Roberts, <a href="https://doi.org/10.1093/comjnl/10.1.74">Multiplicative congruential pseudo-random number generators.</a> The Computer Journal, Volume 10, Issue 1, 74-77.
%H A096550 George S. Fishman and Louis R. Moore, <a href="https://doi.org/10.2307/2287778">A Statistical Evaluation of Multiplicative Congruential Random Number Generators with Modulus 2^31-1</a>, J. American Statistical Assoc., 77, 377 (1982), 129-136.
%H A096550 Pierre L'Ecuyer, <a href="https://dl.acm.org/doi/pdf/10.1145/62959.62969">Efficient and portable combined random number generators</a>, C ACM, 31, 6 (1988), 742-749 and 774.
%H A096550 Pierre L'Ecuyer, <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wsc01rng.pdf">Software for Uniform Random Number Generation: Distinguishing the Good and the Bad.</a> Proceedings of the 2001 Winter Simulation Conference, IEEE Press, Dec. 2001, 95-105.
%H A096550 P. A. W. Lewis, A. S. Goodman and J. M. Miller, <a href="https://doi.org/10.1147/sj.82.0136">A pseudo-random number generator for the System/360</a>, IBM Systems Journal, Volume 8 Issue 2, 136-146, 1969.
%H A096550 Stephen K. Park and Keith. W. Miller, <a href="http://www.firstpr.com.au/dsp/rand31/p1192-park.pdf">Random Number Generators: Good Ones are Hard to Find</a>, Communications of the ACM, Volume 31, Number 10 (October, 1988), 1192-1201.
%H A096550 B. D. Ripley, <a href="https://doi.org/10.2307/1402590">Computer Generation of Random Variables: A Tutorial</a>, International Statistical Review, 51 (1983), 301-309.
%H A096550 B. D. Ripley, <a href="https://doi.org/10.1016/0377-0427(90)90346-2">Thoughts on pseudorandom number generators</a>, J of Computational and Applied Mathematics, 31, 1 (1990), 153-163.
%H A096550 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers.</a>
%F A096550 a(1)=1, a(n) = 7^5 * a(n-1) mod (2^31-1). The sequence is periodic with period length 2^31-2.
%p A096550 a:= proc(n) option remember; `if`(n<2, n,
%p A096550       irem(16807 *a(n-1), 2147483647))
%p A096550     end:
%p A096550 seq(a(n), n=1..30);  # _Alois P. Heinz_, Jun 10 2014
%t A096550 NestList[Mod[#*16807, 2^31 - 1] &, 1, 50] (* _Paolo Xausa_, Aug 29 2024 *)
%o A096550 (C++)
%o A096550 #include <iostream>
%o A096550 #include <random>
%o A096550 void A096550(int max)
%o A096550 {
%o A096550   std::minstd_rand0 gen;
%o A096550   std::cout << "1 1\n";
%o A096550   for (int i = 2; i <= max; ++i)
%o A096550     std::cout << i << ' ' << gen() << '\n';
%o A096550 } // _Eric M. Schmidt_, Dec 18 2012
%o A096550 (PARI) A096550(n)=lift(Mod(16807,1<<31-1)^(n-1)) \\ _M. F. Hasler_, May 14 2015
%Y A096550 Cf. A096551-A096561 (other pseudo-random number generators); A061364, A384406.
%K A096550 nonn,easy
%O A096550 1,2
%A A096550 _Hugo Pfoertner_, Jul 18 2004