A382535 Consecutive states of Lehmer's original linear congruential pseudo-random number generator 23*s mod (10^8+1) when started at s=1.

1, 23, 529, 12167, 279841, 6436343, 48035888, 4825413, 10984498, 52643452, 10799384, 48385830, 12874079, 96103815, 10387723, 38917627, 95105413, 87424478, 10762974, 47548400, 93613190, 53103349, 21377015, 91671341, 8440822, 94138905, 65194794, 99480248

Offset: 1

Author

Sean A. Irvine, May 25 2025

Keywords

• nonn
• easy

Comments

Periodic with period 5882352.

This is the first linear congruential pseudo-random number generator described in the literature. As such, it is the forerunner of one of the most widely used techniques for generating pseudo-random numbers.

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..10000
• D. H. Lehmer, Mathematical methods in large-scale computing units, Proceedings of a Second Symposium on Large-Scale Digital Calculating Machinery (1949), 141-146.
• 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. A009967.

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

Programs

Mathematica

NestList[Mod[23*#, 10^8 + 1] &, 1, 50] (* Paolo Xausa, May 26 2025 *)

Formula

a(n) = 23 * a(n-1) mod (10^8+1).