A096550 -id:A096550 - cp's OEIS frontend

A384260 Consecutive internal states of the linear congruential pseudo-random number generator 3373*s mod (2^24-3) when started at s=1.

1, 3373, 11377129, 5569986, 13861431, 13291345, 2993549, 14135764, 15869839, 9657477, 10099488, 7830634, 5395220, 11578168, 12586013, 6272959, 2625114, 12918271, 2905922, 3782514, 7737842, 11174851, 11152025, 1268779, 1402252, 15399143, 15835104, 9936813

Offset: 1

Sean A. Irvine, May 23 2025

Periodic with period 2^22-1.

This generator was recommended by Sharp and Bays for 24-bit floating-point.

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

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

a:= proc(n) option remember; `if`(n<2, n,
      irem(3373*a(n-1), 2^24-3))
    end:
seq(a(n), n=1..28);  # Alois P. Heinz, May 23 2025

NestList[Mod[3373*#, 2^24 - 3] &, 1, 50] (* Paolo Xausa, May 26 2025 *)

a(n) = 3373 * a(n-1) mod (2^24-3).

A384297 Consecutive internal states of the linear congruential pseudo-random number generator for Microsoft QBASIC when started at 1.

Original entry on oeis.org

1, 12640960, 8124035, 4294458, 3961109, 14212996, 790583, 4786718, 4094057, 13179272, 9990699, 13415490, 7932413, 570572, 4960351, 10275238, 9132497, 9049424, 14589651, 14601802, 1367013, 4120340, 807303, 11634222, 13190201, 14415384, 4594811, 1111378

Offset: 1

Sean A. Irvine, May 24 2025

Periodic with period 2^24.

Also used by Visual BASIC (version 6 and earlier).

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Noesis Pty Ltd, VBA's Pseudo Random Number Generator, 2001.
WikiBooks, QBasic/Appendix.
Index entries for sequences related to pseudo-random numbers.

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

NestList[Mod[16598013*# + 12820163, 2^24] &, 1, 50] (* Paolo Xausa, May 27 2025 *)

a(n) = (16598013 * a(n-1) + 12820163) mod 2^24.

A384315 Consecutive internal states of the linear congruential pseudo-random number generator for Demos started at 1.

Original entry on oeis.org

1, 8192, 9317, 9225317, 19706942, 64858329, 25218022, 53630558, 40796927, 52681924, 53134651, 4299603, 62185148, 971592, 41535118, 60983366, 19606857, 50156573, 32119735, 27545333, 62690922, 51199833, 56863186, 18164438, 43380397, 13011312, 34587268, 44612022

Offset: 1

Sean A. Irvine, May 25 2025

Periodic with period 2^26-9318 = 67099546.

Originally defined by Downham and Roberts in 1967, subsequently used in the Demos modelling system in 2003.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Graham Birtwistle, Demos: a system for Discrete Event Modelling on Simula, Jan 2003.
D. Y. Downham and F. D. K. Roberts, Multiplicative congruential pseudo-random number generators, The Computer J., 10, 1 (1967), 74-77
Index entries for sequences related to pseudo-random numbers.

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

a:= proc(n) option remember; `if`(n<2, n,
      irem(2^13*a(n-1), 2^26-9317))
    end:
seq(a(n), n=1..28);  # Alois P. Heinz, May 26 2025

NestList[Mod[2^13*#, 2^26 - 9317] &, 1, 50] (* Paolo Xausa, May 26 2025 *)

a(n) = 2^13 * a(n-1) mod (2^26-9317).

A384346 Consecutive internal states of the linear congruential pseudo-random number generator (4253261*s+12896793) mod 2^24 when started at s=1.

Original entry on oeis.org

1, 372838, 7765191, 4398068, 1141373, 15605682, 6176419, 2364192, 13454009, 15104446, 16260159, 8774412, 449717, 6277770, 831899, 15169464, 15932529, 11656726, 5003959, 16547108, 2409965, 15155298, 11219859, 5857104, 4740393, 4799854, 8198191, 14633532

Offset: 1

Sean A. Irvine, May 27 2025

Periodic with period 2^24.

The numbers on p. 238 of Lien are given by s/2^24 using this generator starting from s=10529929.

David A. Lien, The BASIC Handbook, Compusoft, 1979 (see p. 238).

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Index entries for sequences related to pseudo-random numbers.

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

NestList[Mod[4253261# + 12896793 , 2^24] &,1,27] (* Stefano Spezia, May 27 2025 *)

a(n) = (4253261 * a(n-1) + 12896793) mod 2^24.

A384373 Consecutive internal states of the linear congruential pseudo-random number generator 131075*s mod 2^27 when started at s=1.

Original entry on oeis.org

1, 131075, 786441, 3538971, 14155857, 53084403, 56885977, 131991691, 11540897, 89279715, 29157033, 42513403, 126884849, 110253011, 56425337, 17363563, 133224257, 106202563, 109285705, 102544347, 34347921, 88494771, 87619609, 131917899, 2930913, 38283939

Offset: 1

Sean A. Irvine, May 27 2025

Periodic with period 2^25.

The numbers on p. 142 of Albrecht et al. are given by s/2^27 using this generator starting from s=69782861.

Robert L. Albrecht, LeRoy Finkel, and Jerald R. Brown, BASIC: A Self-Teaching Guide (2nd ed.), John Wiley & Sons, 1978 (see p. 142).

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Index entries for sequences related to pseudo-random numbers.

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

NestList[Mod[131075*#, 2^27] &, 1, 50] (* Paolo Xausa, May 28 2025 *)

a(n) = 131075 * a(n-1) mod 2^27.

A384375 Consecutive internal states of the linear congruential pseudo-random number generator 950706376*s mod (2^31-1) when started at s=1.

Original entry on oeis.org

1, 950706376, 129027171, 1728259899, 365181143, 1966843080, 1045174992, 636176783, 1602900997, 640853092, 429916489, 1671481929, 1285607481, 1066192246, 48796904, 1176434418, 776417870, 861463458, 1543924916, 557508687, 1650650964, 741730640, 1050856373

Offset: 1

Sean A. Irvine, May 28 2025

Periodic with period 2^31-2.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Pierre L'Ecuyer, Efficient and portable combined random number generators, Commun. ACM, 31, 6 (1988), 742-749 and 774.
Index entries for sequences related to pseudo-random numbers.

Cf. A096550, A384397, A384398, A384399, A384400, A384401, A384402.

NestList[Mod[950706376*#, 2^31 - 1] &, 1, 50] (* Paolo Xausa, May 29 2025 *)

a(n) = 950706376 * a(n-1) mod (2^31-1).

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

Original entry on oeis.org

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

Sean A. Irvine, May 30 2025

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.

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).

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Index entries for sequences related to pseudo-random numbers.

Cf. A384448 (same multiplier).

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

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

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

A384516 Consecutive states of the linear congruential pseudo-random number generator 410092949*s mod 2^32 when started at s=1.

Original entry on oeis.org

1, 410092949, 591276217, 536793261, 1444304305, 547738885, 2808452329, 3344283805, 3273327713, 2664493429, 2310230553, 3826173325, 3564649489, 1018219237, 862195785, 3991693181, 2995334337, 122179925, 2916974457, 3784183405, 2873755249, 2538566853, 1541296041

Offset: 1

Sean A. Irvine, Jun 01 2025

Periodic with period 2^30.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Itshak Borosh and Harald Niederreiter, Optimal multipliers for pseudo-random number generation by the linear congruential method, BIT, 23, 1 (1983), 65-74.
George S. Fishman, Multiplicative Congruential Random Number Generators with Modulus 2^beta: An Exhaustive Analysis for beta = 32 and a Partial Analysis for beta = 48, Math. Comp., 54, 189 (1990), 331-344.
Index entries for sequences related to pseudo-random numbers.

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

NestList[Mod[410092949*#, 2^32] &, 1, 50] (*  Paolo Xausa, Jun 04 2025*)

a(n) = 410092949 * a(n-1) mod 2^32.

A384532 Consecutive states of the linear congruential pseudo-random number generator 663608941*s mod 2^32 when started at s=1.

Original entry on oeis.org

1, 663608941, 4216535657, 1508633781, 3546922769, 2333349949, 1227634681, 1132643077, 1351376673, 1919950605, 164855433, 658288213, 1272246321, 3018965725, 1134861849, 1895169701, 3480322625, 1729483693, 3273926313, 2046821365, 1986078033, 2320900477

Offset: 1

Sean A. Irvine, Jun 01 2025

Periodic with period 2^30.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
J. H. Ahrens and U. Dieter, Computer methods for sampling from the exponential and normal distributions, C ACM, 15, 10 (1972), 873-882.
W. Kirby, Machine-Independent Fortran Coding of Lehmer Random Number Generators, US Dept of the Interior Geological Survey, Reston, VA, 1979.
Index entries for sequences related to pseudo-random numbers.

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

NestList[Mod[663608941*#, 2^32] &, 1, 50] (* Paolo Xausa, Jun 04 2025 *)

a(n) = 663608941 * a(n-1) mod 2^32.

A384535 Consecutive states of the linear congruential pseudo-random number generator 1566083941*s mod 2^32 when started at s=1.

Original entry on oeis.org

1, 1566083941, 2203506137, 1324822941, 1986974193, 2643373845, 1922267721, 3584877005, 1128752353, 3108566981, 1963571129, 3492736765, 2923407569, 1151276405, 1419902505, 2617346349, 3800993217, 2693642277, 144555417, 3452297309, 2296120241, 111579093

Offset: 1

Sean A. Irvine, Jun 02 2025

Periodic with period 2^30.
Implemented as gsl_waterman14 in the GNU Scientific Library.
Knuth attributes this multiplier to Alan G. Waterman.

Donald E. Knuth, The Art of Computer Programming, Vol 2: Seminumerical Algorithms (3rd ed.), 106-108.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Mark Galassi, Jim Davies, James Theiler, Brian Gough, Gerard Jungman, Michael Booth, and Fabrice Rossi, GNU Scientific Library: Reference Manual, 2003 (see p. 184).
Index entries for sequences related to pseudo-random numbers.

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

NestList[Mod[1566083941*#, 2^32] &, 1, 50] (* Paolo Xausa, Jun 04 2025 *)

a(n) = 1566083941 * a(n-1) mod 2^32.

a(n) == 1 (mod 4).

cp's OEIS Frontend

A384260 Consecutive internal states of the linear congruential pseudo-random number generator 3373*s mod (2^24-3) when started at s=1.

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A384297 Consecutive internal states of the linear congruential pseudo-random number generator for Microsoft QBASIC when started at 1.

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A384315 Consecutive internal states of the linear congruential pseudo-random number generator for Demos started at 1.

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A384346 Consecutive internal states of the linear congruential pseudo-random number generator (4253261*s+12896793) mod 2^24 when started at s=1.

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A384373 Consecutive internal states of the linear congruential pseudo-random number generator 131075*s mod 2^27 when started at s=1.

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A384375 Consecutive internal states of the linear congruential pseudo-random number generator 950706376*s mod (2^31-1) when started at s=1.

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

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A384516 Consecutive states of the linear congruential pseudo-random number generator 410092949*s mod 2^32 when started at s=1.

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