A384194 -id:A384194 - cp's OEIS frontend

A383940 Consecutive states of the linear congruential pseudo-random number generator (25173*s+13849) mod 2^16 when started at s=1.

1, 39022, 61087, 20196, 45005, 3882, 21259, 65216, 19417, 30502, 20919, 26076, 16421, 44130, 63139, 32824, 14513, 51934, 36303, 35284, 8573, 11930, 41787, 65200, 9865, 29590, 743, 39628, 46037, 30162, 47315, 23080, 30049, 20814, 4351, 30916, 22317, 25098

Offset: 1

Sean A. Irvine, May 21 2025

Periodic with period 2^16.

This was a popular generator in the 1980's due to Grogono's book, but the period was too short for serious scientific use.

Peter Grogono, Programming in Pascal (2nd ed.), Addison-Wesley, 1984 (see pp. 136-137).

Sean A. Irvine, Table of n, a(n) for n = 1..10000
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 65536.

Cf. A096550-A096561 (other pseudo-random number generators).
Cf. A384082, A384085, A384150, A384194 (other early generators for Pascal).
Cf. A384220 (similar generator for Smalltalk-80).

NestList[Mod[25173*# + 13849, 2^16] &, 1, 100] (* Paolo Xausa, May 22 2025 *)

a(n) = (25173 * a(n-1) + 13849) mod 2^16.

A384404 Consecutive states of the linear congruential pseudo-random number generator for Turbo Pascal when started at 1.

Original entry on oeis.org

1, 134775814, 3698175007, 870078620, 1172187917, 2884733762, 1368768587, 694906232, 1598751577, 1828254910, 352239543, 2039224980, 303092965, 3611442298, 256513635, 1259699184, 3939707825, 1580146294, 3327160399, 1408429452, 2996491197, 3625686706, 3083712891

Offset: 1

Sean A. Irvine, May 30 2025

Periodic with period 2^32.

Also used by Borland Delphi and Virtual Pascal.

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

Cf. A152960, A383940, A384126, A384150, A384194, A384236, A384339, A384429, A384432.

a:= proc(n) option remember; `if`(n=1, 1,
      irem(134775813*a(n-1)+1, 2^32))
    end:
seq(a(n), n=1..23);  # Alois P. Heinz, May 30 2025

NestList[Mod[134775813*# + 1, 2^32] &, 1, 50] (* Paolo Xausa, Jun 04 2025 *)

a(n) = (134775813 * a(n-1) + 1) mod 2^32.

A384339 Consecutive states of the linear congruential pseudo-random number generator for Berkeley Pascal 3.1 when started at 1.

Original entry on oeis.org

1, 113280614, 518180871, 401789364, 123511293, 522841650, 132082531, 254284640, 306822585, 36791486, 267986559, 195744204, 63672117, 39581194, 434609499, 223082744, 48501361, 535916054, 463875063, 53294308, 487523181, 390617314, 240119379, 401404304, 176021033

Offset: 1

Sean A. Irvine, May 26 2025

Periodic with period 2^29.

The default initial seed is 7774755, but 1 is used here for consistency with other OEIS sequences.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
William N. Joy, Susan L. Graham, Charles B. Haley, Marshall Kirk McKusick, and Peter B. Kessler, Berkeley Pascal's User Manual, Version 3.1, April 1986.
Index entries for sequences related to pseudo-random numbers.

Cf. A383940, A384150, A384194, A384236 (other Pascal generators).

NestList[Mod[62605*# + 113218009, 2^29] &, 1, 50] (* Paolo Xausa, May 27 2025 *)

a(n) = (62605 * a(n-1) + 113218009) mod 2^29.

A384973 Consecutive states of the linear congruential pseudo-random number generator (101*s+1) mod 2^13 when started at s=1.

Original entry on oeis.org

1, 102, 2111, 220, 5837, 7906, 3883, 7160, 2265, 7582, 3927, 3412, 549, 6298, 5315, 4336, 3761, 3030, 2927, 716, 6781, 4946, 8027, 7912, 4489, 2830, 7303, 324, 8149, 3850, 3827, 1504, 4449, 6982, 671, 2236, 4653, 3010, 907, 1496, 3641, 7294, 7607, 6452, 4485

Offset: 1

Sean A. Irvine, Jun 13 2025

Periodic with period 2^13.

Sean A. Irvine, Table of n, a(n) for n = 1..8192
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. A384126, A384152, A384158, A384194.

NestList[Mod[101*# + 1, 2^13] &, 1, 50] (* Paolo Xausa, Jun 18 2025 *)

a(n) = (101*a(n-1) + 1) mod 2^13.

cp's OEIS Frontend

A383940 Consecutive states of the linear congruential pseudo-random number generator (25173*s+13849) mod 2^16 when started at s=1.

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A384404 Consecutive states of the linear congruential pseudo-random number generator for Turbo Pascal when started at 1.

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A384339 Consecutive states of the linear congruential pseudo-random number generator for Berkeley Pascal 3.1 when started at 1.

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Mathematica

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A384973 Consecutive states of the linear congruential pseudo-random number generator (101*s+1) mod 2^13 when started at s=1.

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