A384126 Consecutive states of a linear congruential pseudo-random number generator (93*s+1) mod 2^13 when started at s=1.

1, 94, 551, 2092, 6141, 5866, 4867, 2072, 4281, 4918, 6815, 3012, 1589, 322, 5371, 7984, 5233, 3342, 7703, 3676, 5997, 666, 4595, 1352, 2857, 3558, 3215, 4084, 2981, 6898, 2539, 6752, 5345, 5566, 1543, 4236, 733, 2634, 7395, 7800, 4505, 1174, 2687, 4132, 7445

Offset: 1

Author

Sean A. Irvine, May 19 2025

Keywords

• nonn
• easy

Comments

Periodic with period 8192.

References

• John Konvalina and Stanley Wileman, Programming with Pascal, McGraw-Hill, 1987 (see p. 288).

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.
• Index entries for linear recurrences with constant coefficients, order 8192.

Crossrefs

Cf. A096550-A096561 (other pseudo-random number generators).

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(93*a(n-1)+1, 2^13))
    end:
seq(a(n), n=1..45);  # Alois P. Heinz, May 21 2025

Mathematica

NestList[Mod[93*# + 1, 2^13] &, 1, 100] (* Paolo Xausa, May 22 2025 *)

Formula

a(n) = (93*a(n-1) + 1) mod 2^13.