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

1,2

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.

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A096550, A384406.

Sequence in context: A123705 A237364 A371865 * A251498 A233848 A343077

Adjacent sequences: A383795 A383796 A383797 * A383799 A383800 A383801

Keyword

nonn,easy

Author

Sean A. Irvine, May 28 2025

Status

approved