A383798 Consecutive states of the linear congruential pseudo-random number generator for SIMSCRIPT II when started at 1.

1, 630360016, 1549035330, 264620982, 529512731, 1896697821, 2116530888, 1923129168, 1674201058, 108088067, 859154222, 1946499387, 1377890442, 1382793310, 768302678, 1014576563, 514017889, 2050350098, 1928578391, 863848128, 246801402, 166165530, 709020555

Offset: 1

Author

Sean A. Irvine, May 28 2025

Keywords

• nonn
• easy

Comments

Periodic with period 2^31-2.

References

• P. J. Kiviat, R. Villanueva, and H. Markowitz, The Simscript II Programming Language, Prentice-Hall, 1969.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• 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, Commun. ACM, 31, 6 (1988), 742-749 and 774.
• 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. A096550, A384406.

Programs

Magma

[n le 1 select 1 else 630360016 * Self(n-1) mod (2^31-1): n in [1..30]]; // Vincenzo Librandi, May 29 2025

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(630360016*a(n-1), 2^31-1))
    end:
seq(a(n), n=1..23);  # Alois P. Heinz, May 29 2025

Mathematica

RecurrenceTable[{a[1]==1,a[n]==Mod[a[n-1]*630360016,(2^31-1)]},a,{n,1,30}] (* Vincenzo Librandi, May 29 2025 *)

Formula

a(n) = 630360016 * a(n-1) mod (2^31-1).