A384451 Consecutive states of the linear congruential pseudo-random number generator randq1 from Numerical Recipes when started at 1.

1, 1015568748, 1586005467, 2165703038, 3027450565, 217083232, 1587069247, 3327581586, 2388811721, 70837908, 2745540835, 1075679462, 1814098701, 2536995080, 3594602695, 1009643386, 4212701329, 3697481916, 1403919595, 2931756366, 2282599509, 927463856, 448971087

Offset

1,2

Comments

Periodic with period 2^32.

This generator has widespread usage because it appeared in the popular "Numerical Recipes" series of books. The multiplier 1664525 is due to Knuth and the addend 1013904223 due to Lewis.

References

Donald E. Knuth, The Art of Computer Programming: Vol 2, Seminumerical Algorithms (2nd ed.), 1981 (see Sections 3.2-3.3).

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 284).

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Index entries for sequences related to pseudo-random numbers.

Formula

a(n) = (1664525 * a(n) + 1013904223) mod 2^32.

Mathematica

NestList[Mod[1664525*# + 1013904223, 2^32] &, 1, 50] (* Paolo Xausa, Jun 04 2025 *)

Crossrefs

Cf. A384448 (same multiplier).

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

Sequence in context: A269120 A095733 A239919 * A020666 A074205 A277054

Adjacent sequences: A384448 A384449 A384450 * A384452 A384453 A384454

Keyword

nonn,easy

Author

Sean A. Irvine, May 30 2025

Status

approved