A384610 Consecutive states of the linear congruential pseudo-random number generator (262145*s+3) mod 2^35 when started at s=1.

1, 262148, 1310727, 3145738, 5767181, 9175056, 13369363, 18350102, 24117273, 30670876, 38010911, 46137378, 55050277, 64749608, 75235371, 86507566, 98566193, 111411252, 125042743, 139460666, 154665021, 170655808, 187433027, 204996678, 223346761, 242483276

Offset: 1

Author

Sean A. Irvine, Jun 04 2025

Keywords

• nonn
• easy

Comments

Periodic with period 2^35.

References

• Donald E. Knuth, The Art of Computer Programming, Vol 2: Seminumerical Algorithms (3rd ed.), Addison-Wesley, 1998 (see p. 106).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..10000
• Martin Greenberger, Notes on a New Pseudo-Random Number Generator, J ACM, 8, 2 (1961), 163-167.
• Index entries for sequences related to pseudo-random numbers.

Crossrefs

Cf. A384160, A384387, A384565, A384608.

Cf. A096550-A096561 for other pseudo-random number generators.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      irem(262145*a(n-1)+3, 2^35))
    end:
seq(a(n), n=1..26);  # Alois P. Heinz, Jun 04 2025

Mathematica

NestList[Mod[262145*# + 3, 2^35] &, 1, 30] (* Paolo Xausa, Jun 12 2025 *)

Formula

a(n) = (262145 * a(n-1) + 3) mod 2^35.