A096550 -id:A096550 - cp's OEIS frontend

A096552 Consecutive internal states of the linear congruential pseudo-random number generator MTH$RANDOM that is used in the VAX VMS Library.

0, 1, 69070, 475628535, 3277404108, 772999773, 3877832058, 3821835443, 1662200408, 2044158073, 3788989926, 797919023, 2743624612, 1156259413, 1059494674, 584849259, 786050992, 3369345009, 3077427454, 1200308583, 2654771836, 1692139853, 4052415402, 1850655011

Offset: 1

Hugo Pfoertner, Jul 18 2004

nonn

This generator is a variant of A096551.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
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.
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-A096561 for other pseudo-random number generators.

a:= proc(n) option remember; `if`(n<2, 0,
      irem(69069 *a(n-1)+1, 4294967296))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 10 2014

NestList[Mod[#*69069 + 1, 2^32] &, 0, 50] (* Paolo Xausa, Aug 29 2024 *)

a(1)=0, a(n) = (69069*a(n-1)+1) mod 2^32. The sequence is periodic with period length 2^32. [Corrected based on a comment from Kevin Ryde, Nov 13 2024]

A096554 Output of the linear congruential pseudo-random number generator used in function rand() as described in Kernighan and Ritchie, when seeded with 0.

Original entry on oeis.org

0, 21468, 9988, 22117, 3498, 16927, 16045, 19741, 12122, 8410, 12261, 27052, 5659, 9758, 21087, 25875, 32368, 26233, 15212, 17661, 20496, 8191, 23065, 23471, 32096, 10781, 14596, 23212, 24244, 5661, 514, 25643, 1350, 19576, 8051, 18234, 16882, 13023, 5983, 21166

Offset: 1

Hugo Pfoertner, Jul 18 2004

nonn

This sequence and A061364 are generated by the same algorithm but with different seed: A061364 (as well as A096553 which is the sequence of internal states of the generator) has seed 1, while this sequence has seed 0. [Corrected by Jean-Claude Arbaut, Oct 05 2015]

Brian W. Kernighan and Dennis M. Ritchie, The C Programming Language (Second Edition), Prentice Hall Software Series, 1988, page 46.

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

A061364 is the same generator seeded with 1.

static unsigned int next = 0; int rand( ) { next = next * 1103515245 + 12345; return ((next >>16) & 32767); }

BitShiftRight[NestList[Mod[#*1103515245 + 12345, 2^31] &, 12345, 50], 16] (* Paolo Xausa, Aug 29 2024 *)

x(n) = if(n<1, 0, (1103515245 * x(n-1) + 12345) % (2^31));
vector(100, n, floor(x(n)/2^16)) \\ Altug Alkan, Oct 05 2015

Correction of seed value and second formula from David Fifield, May 23 2024: (Start)
x(0) = 0, x(n) = (1103515245 * x(n-1) + 12345) mod 2^31, a(n) = floor(x(n)/2^16).
a(n) = A061364(n + 1212780038). (End)

Name amended (start at 0) by David Fifield, May 23 2024

A096556 Consecutive internal states of the linear congruential pseudo-random number generator used in the Watcom FORTRAN Function URAND when started with SEED=0.

Original entry on oeis.org

0, 453816693, 2013878382, 1461722811, 653338732, 1830525137, 1741773690, 526418231, 109789464, 1577774445, 1454795974, 1716389619, 180917764, 1381854025, 70154322, 301698031, 2068689712, 1594166885, 1923590686, 579939371, 2056610972, 914297537, 1800695338, 1283998631

Offset: 1

Hugo Pfoertner, Jul 20 2004

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Open Watcom, Sybase Watcom C/C++ and FORTRAN compiler.
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, 0,
      irem(2147437301 * a(n-1) +453816693, 2147483648))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 10 2014

NestList[Mod[#*2147437301 + 453816693, 2^31] &, 0, 50] (* Paolo Xausa, Aug 29 2024 *)

a(1)=0, a(n) = ( 2147437301 * a(n-1) + 453816693 ) mod 2^31. The sequence is periodic with period length 2^31.

A382305 Consecutive internal states of the linear congruential pseudo-random number rand48 for Unix when started at 1.

Original entry on oeis.org

1, 25214903928, 206026503483683, 245470556921330, 105707381795861, 223576932655868, 102497929776471, 87262199322646, 266094224901481, 44061996164032, 147838658590923, 157704700760186, 262146585501693, 99421425265860, 6056585619327, 169186298309406

Offset: 1

Sean A. Irvine, Jun 08 2025

Periodic with period 2^48.
A widely used generator because it is included in POSIX glibc.
Also used internally by Java in java.util.Random.
Also provided by the GNU Scientific Library.

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).
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[25214903917*# + 11, 2^48] &, 1, 30] (* Paolo Xausa, Jun 09 2025 *)

a(n) = (25214903917 * a(n-1) + 11) mod 2^48.

A382684 Consecutive internal states of the linear congruential pseudo-random number generator for BCPL when started at 1.

Original entry on oeis.org

1, 2862137630, 1410400247, 1369397724, 1652384221, 2669374922, 2140954419, 1701427304, 2594835833, 3034226998, 3288120879, 389815220, 357129941, 541493090, 3104757995, 2854522816, 2013295089, 2081295438, 2466720615, 4256030860, 3056739021, 751492090

Offset: 1

Sean A. Irvine, Jun 02 2025

Periodic with period 2^32.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Martin Richards, The BCPL Cintsys and Cintpos User Guide, Univ. of Cambridge, 2025.
Index entries for sequences related to pseudo-random numbers.

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

Cf. A084277 (visible state).

NestList[Mod[2147001325*# + 715136305, 2^32] &, 1, 50] (* Paolo Xausa, Jun 04 2025 *)

a(n) = (2147001325 * a(n-1) + 715136305) mod 2^32.

A383645 Consecutive internal states of the linear congruential pseudo-random number generator (17405*s+10395331) mod 2^24 when started at s=1.

Original entry on oeis.org

1, 10412736, 16578179, 2262842, 2257173, 4251524, 3870775, 3934750, 10123369, 13310344, 356907, 14791746, 14354941, 11842764, 8826975, 14928294, 8608209, 15734096, 7839443, 6803018, 3333093, 7266068, 9654663, 9209390, 10306617, 15070744, 4922491, 5109074

Offset: 1

Sean A. Irvine, May 23 2025

Periodic with period 2^24.

This random number generator was used by some versions of IBM BASIC (Schneider).

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. A096550-A096561 other pseudo-random number generators.

NestList[Mod[17405*# + 10395331, 2^24] &, 1, 50] (* Paolo Xausa, May 26 2025 *)

a(n) = (17405 * a(n-1) + 10395331) mod 2^24.

A384082 Consecutive states of the linear congruential pseudo-random number generator (61*s+323) mod 500 when started at s=1.

Original entry on oeis.org

1, 384, 247, 390, 113, 216, 499, 262, 305, 428, 431, 114, 277, 220, 243, 146, 229, 292, 135, 58, 361, 344, 307, 50, 373, 76, 459, 322, 465, 188, 291, 74, 337, 380, 3, 6, 189, 352, 295, 318, 221, 304, 367, 210, 133, 436, 419, 382, 125, 448, 151, 34, 397, 40

Offset: 1

Sean A. Irvine, May 18 2025

Periodic with period length 500.

Originally defined by Lamie in the form (61*s+2323) mod 500, even though 2323 > 500.

Edward L. Lamie, Pascal Programming, John Wiley and Sons, 1987 (see p. 150).

Sean A. Irvine, Table of n, a(n) for n = 1..500
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.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 500.

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

a:= proc(n) option remember; `if`(n<2, n,
      irem(61*a(n-1)+323, 500))
    end:
seq(a(n), n=1..54);  # Alois P. Heinz, May 21 2025

NestList[Mod[61*# + 323, 500] &, 1, 100] (* Paolo Xausa, May 19 2025 *)

a(n) = (61*a(n-1) + 323) mod 500.

A384085 Consecutive states of the linear congruential pseudo-random number generator (40*s+725) mod 729 when started at s=1.

Original entry on oeis.org

1, 36, 707, 574, 357, 425, 229, 408, 278, 181, 675, 23, 187, 186, 146, 4, 156, 404, 118, 342, 554, 286, 501, 353, 265, 390, 287, 541, 495, 113, 142, 573, 317, 283, 381, 656, 721, 405, 158, 484, 402, 38, 58, 129, 53, 658, 72, 689, 583, 717, 245, 319, 363, 665

Offset: 1

Sean A. Irvine, May 18 2025

Periodic with period 729.

Originally defined by Savitch in the form (40*s+3641) mod 729, even though 3641 > 729.

Walter J. Savitch, Pascal: An Introduction to the Art and Science of Programming, Benjamin Cummings, 1984 (see p. 244).

Sean A. Irvine, Table of n, a(n) for n = 1..729
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.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 729.

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

a:= proc(n) option remember; `if`(n<2, n,
      irem(40*a(n-1)+725, 729))
    end:
seq(a(n), n=1..54);  # Alois P. Heinz, May 18 2025

NestList[Mod[40*# + 725, 729] &, 1, 100] (* Paolo Xausa, May 22 2025 *)

a(n) = (40*a(n-1) + 725) mod 729.

A384220 Consecutive states of the linear congruential pseudo-random number generator for Smalltalk-80 when started at 1.

Original entry on oeis.org

1, 41030, 24167, 29748, 11069, 4562, 19459, 53408, 8761, 54302, 60255, 60364, 8437, 29482, 55419, 12728, 9073, 15094, 28503, 52836, 58797, 14210, 52211, 44496, 58281, 13518, 51791, 31740, 22885, 48858, 1643, 42216, 17121, 8614, 56391, 21652, 23581, 26930

Offset: 1

Sean A. Irvine, May 22 2025

Periodic with period 2^16.

This generator was widely used with Smalltalk-80 due to the Goldberg and Robson book.

Adele Goldberg and David Robson, Smalltak-80: The Language and Its Implementation, Addison-Wesley, 1983 (see p. 152).

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 65536.

Cf. A383940 (similar generator for Pascal).

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

NestList[Mod[27181*# + 13849, 2^16] &, 1, 50] (* Paolo Xausa, May 23 2025 *)

a(n) = (27181 * a(n-1) + 13849) mod 2^16.

A384316 Consecutive states of the linear congruential pseudo-random number generator 3125*s mod 2^26 when started at s=1.

Original entry on oeis.org

1, 3125, 9765625, 50153869, 31643185, 33596453, 30652329, 24179197, 62518625, 16800021, 20933977, 54644589, 39390609, 17996549, 1987593, 37212637, 56938177, 26204661, 16751545, 3664205, 42133745, 361957, 57373801, 45352381, 59378721, 2494165, 9637401, 52107053

Offset: 1

Sean A. Irvine, May 25 2025

Periodic with period 2^24 (considerably less than the modulus).

Sean A. Irvine, Table of n, a(n) for n = 1..10000
M. C. Pike and I. D. Hill, Algorithm 266: pseudo-random numbers [G5], Commun. ACM, 8, 10 (1965), p. 605.
Index entries for sequences related to pseudo-random numbers.

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

NestList[Mod[3125*#, 2^26] &, 1, 50] (* Paolo Xausa, May 27 2025 *)

a(n) = 3125 * a(n-1) mod 2^26.

cp's OEIS Frontend

A096552 Consecutive internal states of the linear congruential pseudo-random number generator MTH$RANDOM that is used in the VAX VMS Library.

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A096554 Output of the linear congruential pseudo-random number generator used in function rand() as described in Kernighan and Ritchie, when seeded with 0.

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A096556 Consecutive internal states of the linear congruential pseudo-random number generator used in the Watcom FORTRAN Function URAND when started with SEED=0.

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A382305 Consecutive internal states of the linear congruential pseudo-random number rand48 for Unix when started at 1.

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A382684 Consecutive internal states of the linear congruential pseudo-random number generator for BCPL when started at 1.

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A383645 Consecutive internal states of the linear congruential pseudo-random number generator (17405*s+10395331) mod 2^24 when started at s=1.

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A384082 Consecutive states of the linear congruential pseudo-random number generator (61*s+323) mod 500 when started at s=1.

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A384085 Consecutive states of the linear congruential pseudo-random number generator (40*s+725) mod 729 when started at s=1.