A384194 Consecutive states of the linear congruential pseudo-random number generator 259*s mod 2^15 when started at s=1.

1, 259, 1545, 6939, 27729, 5619, 13529, 30603, 29089, 30179, 17577, 30459, 24561, 4307, 1401, 2411, 1857, 22211, 18249, 7899, 14225, 14259, 23065, 10059, 16609, 9123, 3561, 4795, 29489, 2707, 12985, 20779, 7809, 23683, 6281, 21147, 4817, 2419, 3929, 1803, 8225

Offset: 1

Author

Sean A. Irvine, May 21 2025

Keywords

• nonn
• easy

Comments

Periodic with period 8192 (considerably less than the modulus).

A 16-bit version of RANDU (A096555) that suffers from all the same problems.

References

• Byron S. Gottfried, Schaum's Outline of Theory and Problems of Programming with Pascal, McGraw-Hill, 1985 (see p. 143).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..8192
• Stephen K. Park and Keith W. Miller, Random number generators: good ones are hard to find, Communications of the ACM, Vol 31, 10 (1988), 192-201.
• W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
• Index entries for sequences related to pseudo-random numbers.

Crossrefs

Cf. A096555, A384158.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(259*a(n-1), 2^15))
    end:
seq(a(n), n=1..41);  # Alois P. Heinz, May 21 2025

Mathematica

NestList[Mod[259*#, 2^15] &, 1, 100] (* Paolo Xausa, May 22 2025 *)

Formula

a(n) = 259 * a(n-1) mod 2^15.