A096550 -id:A096550 - cp's OEIS frontend

A384405 Consecutive internal states of the linear congruential pseudo-random number generator 69621 * s mod (2^31-1) when started at s=1.

1, 69621, 552116347, 1082396834, 201323037, 1832878655, 1219051368, 874078441, 971035822, 1699755902, 1619285207, 1953863635, 1883480414, 143449980, 1332099030, 837788288, 2002546328, 344571154, 1995975644, 300997201, 580703395, 623924873, 1121855264

Offset: 1

Sean A. Irvine, May 27 2025

Periodic with period 2^31-2.

Presented by Carta as an alternative to Park and Miller's Minimal Standard Generator.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
David G. Carta, Two Fast Implementations of the "Minimal Standard" Random Number Generator, C ACM, 33, 1 (1990), 87-88.
Index entries for sequences related to pseudo-random numbers.

Cf. A096550, A384404.

NestList[Mod[69621*#, 2^31 - 1] &, 1, 50] (* Paolo Xausa, Jun 04 2025 *)

a(n) = 69621 * a(n-1) mod (2^31-1).

A384448 Consecutive states of the linear congruential pseudo-random number generator for the INMOS Transputer when started at 1.

Original entry on oeis.org

1, 1664525, 389569705, 2940799637, 158984081, 2862450781, 3211393721, 1851289957, 3934847009, 2184914861, 246739401, 1948736821, 2941245873, 4195587069, 4088025561, 980655621, 2001863745, 657792333, 65284841, 1282409429, 3808694225, 2968195997, 2417331449

Offset: 1

Sean A. Irvine, May 29 2025

Periodic with period 2^30.

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

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

NestList[Mod[1664525*#, 2^32] &, 1, 50] (* Paolo Xausa, May 30 2025 *)

a(n) = 1664525 * a(n-1) mod 2^32.

A384567 Consecutive states of the linear congruential pseudo-random number generator for the Atari ST when started at 1.

Original entry on oeis.org

1, 3141592622, 1588972055, 1279602700, 1481914909, 3913565466, 2610266515, 1903286488, 936717817, 3104230086, 4091513039, 469042788, 2999973781, 54420274, 4053162955, 3383133360, 3380310769, 456637022, 465319559, 936566716, 2283027469, 2613197898, 63902979

Offset: 1

Sean A. Irvine, Jun 03 2025

Periodic with period 2^32.

Megamax Inc., Laser C: C Language Development System, Atari ST, 1988 (see p. 514).

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.
Index entries for sequences related to pseudo-random numbers.

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

NestList[Mod[3141592621*# + 1, 2^32] &, 1, 50] (* Paolo Xausa, Jun 05 2025 *)

a(n) = (3141592621 * a(n-1) + 1) mod 2^32.

A384608 Consecutive states of the linear congruential pseudo-random number generator (129*s+27098671125) mod 2^35 when started at s=1.

Original entry on oeis.org

1, 27098671254, 18133949355, 29915928896, 3603063125, 10857477098, 18963943679, 33905981588, 2923784873, 26309797694, 19448475219, 27691073512, 25834363901, 26836992658, 18737148839, 4649447228, 8402072913, 11454449126, 27253858555, 3793372816, 1047688869

Offset: 1

Sean A. Irvine, Jun 04 2025

Periodic with period 2^35.

The first set of numbers on p. 156 of Hirsh is reproduced by s/2^35 starting with s=4818528277.

Seymour C. Hirsh, BASIC Programming Self-Taught, Reston Pub Co, Reston, VA, 1980 (see p. 156).
Donald E. Knuth, The Art of Computer Programming, Vol 2: Seminumerical Algorithms (3rd ed.), Addison-Wesley, 1998 (see p. 106).

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

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

Cf. A384387, A384565.

a:= proc(n) option remember; `if`(n<2, n,
      irem(129*a(n-1)+27098671125, 2^35))
    end:
seq(a(n), n=1..21);  # Alois P. Heinz, Jun 04 2025

NestList[Mod[129*# + 27098671125, 2^35] &, 1, 30] (* Paolo Xausa, Jun 12 2025 *)

a(n) = (129*a(n-1) + 27098671125) mod 2^35.

A384643 Consecutive states of the linear congruential pseudo-random number generator for Simula on the UNIVAC when started at 1.

Original entry on oeis.org

1, 30517578125, 4728272809, 14042552597, 5475208593, 22652899805, 14780701625, 12079957477, 33211157537, 21459834669, 11626649801, 22641538997, 32099503025, 31057406333, 28470525657, 2272198277, 31308848193, 23703460045, 6636903913, 5151124053, 2502905297

Offset: 1

Sean A. Irvine, Jun 05 2025

Periodic with period 2^33.

UNIVAC 1106/1108 SIMULA Programmer Reference, UP-7556 Rev. 1, (1971).

Sean A. Irvine, Table of n, a(n) for n = 1..10000
L. Peter Jennergren, Another method for random number generation on microcomputers, Simulation, 41, 2 (1983), p. 79.
Index entries for sequences related to pseudo-random numbers.

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

NestList[Mod[5^15*#, 2^35] &, 1, 30] (* Paolo Xausa, Jun 12 2025 *)

a(n) = 5^15 * a(n-1) mod 2^35.

A384935 Consecutive states of the linear congruential pseudo-random number generator 513*s mod (2^31-1) when started at s=1.

Original entry on oeis.org

1, 513, 263169, 135005697, 538445857, 1344817825, 549293538, 467227237, 1316887764, 1253557774, 977527609, 1107973666, 1454807850, 1139601541, 500038549, 969221644, 1141980915, 1720657411, 81472926, 993421745, 671730846, 1000540478, 28673581, 1824645171

Offset: 1

Sean A. Irvine, Jun 12 2025

Periodic with period 2^31-2.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
B. D. Ripley, Computer Generation of Random Variables: A Tutorial, International Statistical Review, 51 (1983), 301-309.
Alan Tootill, PCW Subset, Personal Computer World, September 1982, see p. 173.
Index entries for sequences related to pseudo-random numbers.

Cf. A096550.

NestList[Mod[513*#, 2^31 - 1] &, 1, 30] (* Paolo Xausa, Jun 13 2025 *)

a(n) = 513 * a(n-1) mod (2^31-1).

A096559 Consecutive states of a linear congruential pseudo-random number generator that has the spectrally best primitive root for 2^31-1 as multiplier.

Original entry on oeis.org

1, 62089911, 847344462, 1061653656, 1954074819, 226824280, 953102500, 1452288378, 50913524, 2133871779, 1843965925, 427233754, 195855103, 1546822229, 1652729917, 1636805220, 217994169, 1312006067, 208869911, 310792805, 675992938, 1109700100, 855351136, 863373758

Offset: 1

Hugo Pfoertner, Aug 14 2004

nonn

The results of the spectral tests for this generator are given in line 18 of Table 1 in D. Knuth's TAOCP vol. 2, page 106.

G. A. Fishman, L. R. Moore III; An exhaustive analysis of multiplicative congruential random number generators with modulus 2^31-1. SIAM Journal on Scientific and Statistical Computing, Volume 7, Issue 1 (1986), 24-45. Erratum, ibid, Vol. 7, Issue 3 (1986) p. 1058.
D. E. Knuth, The Art of Computer Programming Third Edition. Vol. 2 Seminumerical Algorithms. Chapter 3.3.4 The Spectral Test, Page 108. Addison-Wesley 1997.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index entries for sequences related to pseudo-random numbers.

Cf. A096550-A096561, A061364.

a:= proc(n) option remember; `if`(n<2, n,
      irem(62089911 *a(n-1), 2147483647))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 10 2014

NestList[Mod[#*62089911, 2^31 - 1] &, 1, 50] (* Paolo Xausa, Aug 29 2024 *)

a(n)=lift(Mod(62089911,2147483647)^(n-1)) \\ M. F. Hasler, May 14 2015

a(1)=1, a(n)=62089911*a(n-1) mod (2^31-1).

A383798 Consecutive states of the linear congruential pseudo-random number generator for SIMSCRIPT II when started at 1.

Original entry on oeis.org

1, 630360016, 1549035330, 264620982, 529512731, 1896697821, 2116530888, 1923129168, 1674201058, 108088067, 859154222, 1946499387, 1377890442, 1382793310, 768302678, 1014576563, 514017889, 2050350098, 1928578391, 863848128, 246801402, 166165530, 709020555

Offset: 1

Sean A. Irvine, May 28 2025

Periodic with period 2^31-2.

P. J. Kiviat, R. Villanueva, and H. Markowitz, The Simscript II Programming Language, Prentice-Hall, 1969.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
George S. Fishman and Louis R. Moore, A Statistical Evaluation of Multiplicative Congruential Random Number Generators with Modulus 2^31-1, J American Statistical Assoc., 77, 377 (1982), 129-136.
Pierre L'Ecuyer, Efficient and portable combined random number generators, Commun. ACM, 31, 6 (1988), 742-749 and 774.
B. D. Ripley, Computer Generation of Random Variables: A Tutorial, International Statistical Review, 51 (1983), 301-309.
B. D. Ripley, Thoughts on pseudorandom number generators, J of Computational and Applied Mathematics, 31, 1 (1990), 153-163.
Index entries for sequences related to pseudo-random numbers.

Cf. A096550, A384406.

[n le 1 select 1 else 630360016 * Self(n-1) mod (2^31-1): n in [1..30]]; // Vincenzo Librandi, May 29 2025

a:= proc(n) option remember; `if`(n<2, n,
      irem(630360016*a(n-1), 2^31-1))
    end:
seq(a(n), n=1..23);  # Alois P. Heinz, May 29 2025

RecurrenceTable[{a[1]==1,a[n]==Mod[a[n-1]*630360016,(2^31-1)]},a,{n,1,30}] (* Vincenzo Librandi, May 29 2025 *)

a(n) = 630360016 * a(n-1) mod (2^31-1).

A383956 Consecutive states of the linear congruential pseudo-random number generator used by BASIC on the Poly-1 computer when started at 1.

Original entry on oeis.org

1, 7771826, 12906479, 12752200, 14370573, 4177230, 16102619, 5888068, 8967385, 14199722, 1838727, 7559424, 14513509, 9092550, 15771891, 2282364, 11580593, 15929250, 14479391, 2474936, 6872765, 1998142, 6754315, 6251956, 4652937, 6660762, 6157495, 1357168

Offset: 1

Sean A. Irvine, May 15 2025

The sequence is periodic with period 2^24.

In Poly-1 BASIC, random numbers were generated with the RND(m) function. With RND(0) the internal state was returned as a floating-point number state/2^24, otherwise the state was return modulo m.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Andrew Trotman, The Poly Preservation Project
Wikipedia, Poly-1
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(4253261*a(n-1)+3518565, 2^24))
    end:
seq(a(n), n=1..28);  # Alois P. Heinz, May 21 2025

NestList[Mod[4253261*# + 3518565, 2^24] &, 1, 50] (* Paolo Xausa, May 22 2025 *)

a(n) = (4253261 * a(n-1) + 3518565) mod 2^24.

A384240 Consecutive states of the linear congruential pseudo-random number generator (2897*s + 1) mod 2^23 when started at s=1.

Original entry on oeis.org

1, 2898, 6899, 3209188, 2439973, 5393846, 6383767, 5280968, 6531913, 6640922, 3672891, 3610284, 6787181, 7954814, 1589983, 834960, 2960017, 2011874, 6705027, 4835700, 47541, 3508550, 5665063, 3570264, 8289753, 7218346, 7137227, 7016508, 1226493, 4769038

Offset: 1

Sean A. Irvine, May 22 2025

Periodic with period 2^23.

M. R. Eagle, Introduction to BASIC, 1976.

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[2897*# + 1, 2^23] &, 1, 50] (* Paolo Xausa, May 23 2025 *)

a(n) = (2897 * a(n-1) + 1) mod 2^23.

cp's OEIS Frontend

A384405 Consecutive internal states of the linear congruential pseudo-random number generator 69621 * s mod (2^31-1) when started at s=1.

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A384448 Consecutive states of the linear congruential pseudo-random number generator for the INMOS Transputer when started at 1.

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A384567 Consecutive states of the linear congruential pseudo-random number generator for the Atari ST when started at 1.

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A384608 Consecutive states of the linear congruential pseudo-random number generator (129*s+27098671125) mod 2^35 when started at s=1.

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A384643 Consecutive states of the linear congruential pseudo-random number generator for Simula on the UNIVAC when started at 1.

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A384935 Consecutive states of the linear congruential pseudo-random number generator 513*s mod (2^31-1) when started at s=1.

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A096559 Consecutive states of a linear congruential pseudo-random number generator that has the spectrally best primitive root for 2^31-1 as multiplier.

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Programs

Maple

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A383798 Consecutive states of the linear congruential pseudo-random number generator for SIMSCRIPT II when started at 1.

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