A384289 -id:A384289 - cp's OEIS frontend

A384290 Consecutive internal states of the linear congruential pseudo-random number generator (214013*s+10395331) mod 2^24 when started at s=1.

1, 10609344, 3405443, 427834, 2388245, 7987076, 1839159, 4065822, 15628393, 661896, 14709291, 13743170, 13699581, 13219020, 11251807, 9554342, 7035345, 11212112, 3579603, 10735178, 6085605, 10477332, 3953031, 2524718, 5850169, 6092312, 3021947, 1439058

Offset: 1

Sean A. Irvine, May 24 2025

Periodic with period 2^24.

Used by some versions of IBM BASIC.

David I. Schneider, Handbook of BASIC (3rd ed.), Simon & Schuster, 1988 (see p. 497).

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. A383645, A384289, A384291.

NestList[Mod[214013*# + 10395331, 2^24] &, 1, 50] (* Paolo Xausa, May 27 2025 *)

a(n) = (214013 * a(n-1) + 10395331) mod 2^24.

A384291 Consecutive internal states of the linear congruential pseudo-random number generator (214013*s+13737667) mod 2^24 when started at s=1.

Original entry on oeis.org

1, 13951680, 13497987, 7046970, 2650389, 10542980, 14290999, 3607070, 3569769, 6625672, 160299, 10400834, 10291709, 10007756, 7450719, 7522726, 16472529, 3020112, 14720723, 14208586, 15784933, 1498900, 676231, 15697454, 3228729, 521752, 6298747, 11728210

Offset: 1

Sean A. Irvine, May 24 2025

Periodic with period 2^24.

Used by some versions of IBM BASIC.

David I. Schneider, Handbook of BASIC (3rd ed.), Simon & Schuster, 1988 (see p. 497).

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. A384289, A384290.

NestList[Mod[214013*# + 13737667, 2^24] &, 1, 50] (* Paolo Xausa, May 27 2025 *)

a(n) = (214013 * a(n-1) + 13737667) mod 2^24.

A084275 Pseudo-random numbers: MS C 6.0 version.

Original entry on oeis.org

41, 18467, 6334, 26500, 19169, 15724, 11478, 29358, 26962, 24464, 5705, 28145, 23281, 16827, 9961, 491, 2995, 11942, 4827, 5436, 32391, 14604, 3902, 153, 292, 12382, 17421, 18716, 19718, 19895, 5447, 21726, 14771

Offset: 0

Frank Ellermann, May 20 2003

Zhuorui He, Table of n, a(n) for n = 0..10000 (terms 0..98 from Alan Klette).
Sean A. Irvine, Java program (github)
Index entries for sequences related to pseudo-random numbers.

Cf. A084276, A084277, A096557, A096558, A061364, A384289.

#include 
int main()
{
    long next = 1;
    int i = 0;
    while ( i++ < 33 )
    {
        next = next * 214013L + 2531011L;
        printf( "%d ", (unsigned)( next >> 16) & 0x7FFF );
    }
    printf("\n");
    return 0;
}

a(n) = A096558(n+199670977) = floor((A096557(n+199670977) mod 2^31)/2^16). - Zhuorui He, Aug 22 2025

Corrected by Alan Klette, Jun 09 2019

A384292 Consecutive internal states of the linear congruential pseudo-random number generator (214013*s+13523655) mod 2^24 when started at s=1.

Original entry on oeis.org

1, 13737668, 13733499, 10705750, 2695365, 5655672, 8607071, 956074, 10862281, 15041132, 426883, 3316798, 7405069, 1954976, 13589735, 12754962, 4276881, 7083796, 15164811, 11671078, 798805, 8347080, 9527663, 4764282, 13282137, 16579772, 2970771, 7760142

Offset: 1

Sean A. Irvine, May 24 2025

Periodic with period 2^24.

Intended as a generator in IBM BASIC, but was actually implemented incorrectly as (214013 * (s mod 2^16) + 13523655) mod 2^24 (see A384293) resulting in a period of just 2^16.

G. Sawitzki, Another random number generator which should be avoided, Statistical Software Newsletter, 11 (1985), 81-82.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
B. D. Ripley, Thoughts on pseudorandom number generators, J of Computational and Applied Mathematics, 31, 1 (1990), 153-163.
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. A384289, A384290, A384291, A384292.

NestList[Mod[214013*# + 13523655, 2^24] &, 1, 50] (* Paolo Xausa, May 27 2025 *)

a(n) = (214013 * a(n-1) + 13523655) mod 2^24.

A384293 Consecutive internal states of the pseudo-random number generator (214013*(s mod 2^16)+13523655) mod 2^24 when started at s=1.

Original entry on oeis.org

1, 13737668, 4492923, 1465174, 1188037, 13716600, 8738143, 9934506, 13614793, 13927020, 11895683, 4496446, 458253, 7197856, 2514151, 3121170, 8864401, 3086100, 2844043, 6755878, 2240597, 10706376, 942447, 16495226, 10660697, 5962940, 2184339, 16607502

Offset: 1

Sean A. Irvine, May 24 2025

Periodic with period 2^16 (note 1 is not part of the repeating cycle).

This generator was used in IBM BASIC and was an erroneous attempt to implement (214013*s+13523655) mod 2^24 (see A384292).

G. Sawitzki, Another random number generator which should be avoided, Statistical Software Newsletter, 11 (1985), 81-82.

Sean A. Irvine, Table of n, a(n) for n = 1..65537
B. D. Ripley, Thoughts on pseudorandom number generators, J of Computational and Applied Mathematics, 31, 1 (1990), 153-163.
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. A384289, A384290, A384291, A384292.

NestList[Mod[214013*Mod[#, 2^16] + 13523655, 2^24] &, 1, 50] (* Paolo Xausa, May 27 2025 *)

a(n) = (214013 * (s mod 2^16) + 13523655) mod 2^24.

A384331 Consecutive internal states of a linear congruential pseudo-random number generator for Microsoft C and C++ when started at 1.

Original entry on oeis.org

1, 2745024, 1210316419, 415139642, 1736732949, 1256316804, 1030492215, 752224798, 1924036713, 1766988168, 1603301931, 373929026, 1844513277, 1525789900, 1102819423, 652855718, 32201169, 196285776, 782671571, 316395082, 356309989, 2122833684, 957108615

Offset: 1

Sean A. Irvine, May 28 2025

Periodic with period 2^31.

Also used by Microsoft Quick C.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Guglielmo Morgari, Randomness Tests for Binary Sequences, PhD Thesis, Univ. of Torino, 2023.
Wikipedia, Linear congruential generator
Index entries for sequences related to pseudo-random numbers.

Cf. A384289 (24-bit modulus), A096557 (32-bit modulus).

[n le 1 select 1 else (214013 * Self(n-1) + 2531011) mod 2^31: n in [1..30]]; // Vincenzo Librandi, May 29 2025

NestList[Mod[214013*#+2531011,2^31]&,1,27] (* Vincenzo Librandi, May 29 2025 *)

a(n) = (214013 * a(n-1) + 2531011) mod 2^31.

cp's OEIS Frontend

A384290 Consecutive internal states of the linear congruential pseudo-random number generator (214013*s+10395331) mod 2^24 when started at s=1.

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A384291 Consecutive internal states of the linear congruential pseudo-random number generator (214013*s+13737667) mod 2^24 when started at s=1.

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A084275 Pseudo-random numbers: MS C 6.0 version.

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A384292 Consecutive internal states of the linear congruential pseudo-random number generator (214013*s+13523655) mod 2^24 when started at s=1.

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A384293 Consecutive internal states of the pseudo-random number generator (214013*(s mod 2^16)+13523655) mod 2^24 when started at s=1.

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Programs

Mathematica

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A384331 Consecutive internal states of a linear congruential pseudo-random number generator for Microsoft C and C++ when started at 1.

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Magma

Mathematica

Formula