A383809 -id:A383809 - cp's OEIS frontend

A384113 Consecutive states of a linear congruential pseudo-random number generator for MacModula-2 when started at 1.

1, 13, 169, 2197, 829, 1533, 1441, 245, 874, 2118, 2113, 2048, 1203, 1773, 2250, 1518, 1246, 21, 273, 1238, 2228, 1232, 2150, 218, 523, 2177, 569, 464, 1410, 2153, 257, 1030, 1835, 745, 441, 1111, 577, 568, 451, 1241, 2267, 1739, 1808, 394, 500, 1878, 1304

Offset: 1

Sean A. Irvine, May 19 2025

An example of a terrible random number generator.

Periodic with period 1155 (well below the modulus 2311).

Modula Corporation, MacModula-2 System Reference Manual, 1985 (see p. 41).

Sean A. Irvine, Table of n, a(n) for n = 1..1155
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 1155.

Cf. A001022.
Cf. A096550-A096561 other pseudo-random number generators.
Cf. A383809 (another generator with a similar problem).

a:= proc(n) option remember; `if`(n<2, n,
      irem(13*a(n-1), 2311))
    end:
seq(a(n), n=1..47);  # Alois P. Heinz, May 21 2025

NestList[Mod[13*#, 2311] &, 1, 100] (* Paolo Xausa, May 22 2025 *)

my(f=Mod(13,2311)); a(n) = lift(f^((n-1) % 1155)); \\ Kevin Ryde, May 25 2025

a(n) = 13 * a(n-1) mod 2311.

A384152 Consecutive states of the linear congruential pseudo-random number generator used by OMNITAB II when started at 1.

Original entry on oeis.org

1, 125, 7433, 3429, 2641, 2445, 2521, 3829, 3489, 1949, 6057, 3461, 6641, 2733, 5753, 6421, 8001, 701, 5705, 421, 3473, 8141, 1817, 5941, 5345, 4573, 6377, 2501, 1329, 2285, 7097, 2389, 3713, 5373, 8073, 1509, 209, 1549, 5209, 3957, 3105, 3101, 2601, 5637, 113

Offset: 1

Sean A. Irvine, May 20 2025

Periodic with period length 2048.
A terrible generator with period much less than the modulus.
Also, RN5 of the IRCCRAND package.
Originally defined by Kruskal including the implementation s = 5*s mod 8192; s = 5*s mod 8192; s = 5*s mod 8192 (rather than s = 125*s mod 8192).

Sean A. Irvine, Table of n, a(n) for n = 1..2048
Edward J. Dudewicz, IRCCRAND - The Ohio State University Random Number Generator Package, Technical Report, 1974.
David Hogben, Sally T. Peavy, and Ruth N. Varner, OMNITAB II: User's Reference Manual, NBS Technical Note 552, 1971.
J. B. Kruskal, Extremely portable random number generator, Communications of the ACM, 12, 2 (1969), 93-94.
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 2048.

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

Cf. A383809, A384113, A384126, A384971, A384973 (other examples with short periods).

a:= proc(n) option remember; `if`(n<2, n,
      irem(125*a(n-1), 2^13))
    end:
seq(a(n), n=1..45);  # Alois P. Heinz, May 21 2025

NestList[Mod[125*#, 2^13] &, 1, 100] (* Paolo Xausa, May 21 2025 *)

a(n) = lift(Mod(5,8192)^(3*n-3)) \\ Jianing Song, Jul 06 2025

a(n) = 125 * a(n-1) mod 2^13.

A384361 Consecutive internal states of the linear congruential pseudo-random number generator of the HP 48 series calculators when started at 999500333083533.

Original entry on oeis.org

999500333083533, 529199358633911, 43582181444437, 294922982088079, 41089642444893, 284830972469031, 786870433805477, 40703079813759, 869103111377453, 156083179654551, 561556952003317, 315753873725039, 722319935785213, 518159379358471, 201897051493957, 715330849773919

Offset: 1

Paolo Xausa, May 27 2025

The initial 999500333083533 seed is the one used by the calculators after a memory clean; successive executions of the RAND command give the terms of this sequence (divided by 10^15 and truncated to 12 significant digits).
See links for more information.

Paolo Xausa, Table of n, a(n) for n = 1..10000
John Meyers, Random thoughts on HP48 random functions, comp.sys.hp48 Google group, 1997.
Steve VanDevender and Detlef Mueller, How RAND Works, hpcalc.org, 1992.
Index entries for sequences related to pseudo-random numbers.

Cf. A384416 (starting at 1).

Cf. other pseudo-random number generators: A096550-A096561, A381318, A382535, A383809, A384081, A384221.

NestList[Mod[2851130928467*#, 10^15] &, 999500333083533, 15]

a(1) = 999500333083533; for n > 1, a(n) = 2851130928467*a(n-1) mod 10^15.

A384416 Consecutive internal states of the linear congruential pseudo-random number generator of the HP 48 series calculators when started at 1.

Original entry on oeis.org

1, 2851130928467, 261097470970089, 335429755623563, 468090732667921, 287888716607107, 194022960814969, 298923961822523, 84062462462241, 191517259514547, 165777802909449, 436661297384683, 996040654470961, 669370619746787, 188023750085529, 201468430854043, 677208350742081

Offset: 1

Paolo Xausa, May 28 2025

To initialize the seed to 1, use the RDZ command with an argument between 10^-16 and 10^-13 (for example, "1E-13 RDZ"). Successive executions of the RAND command give the terms of this sequence (divided by 10^15 and truncated to 12 significant digits).
After a memory clean, the calculators use the seed 999500333083533 (cf. A384361).
See the Meyers link for more information.
Periodic with period 10^14/2.

Paolo Xausa, Table of n, a(n) for n = 1..10000
John Meyers, Random thoughts on HP48 random functions, comp.sys.hp48 Google group, 1997.
Steve VanDevender and Detlef Mueller, How RAND Works, hpcalc.org, 1992.
Index entries for sequences related to pseudo-random numbers.

Cf. A384361 (starting at the default seed).

Cf. other pseudo-random number generators: A096550-A096561, A381318, A382535, A383809, A384081, A384221.

NestList[Mod[2851130928467*#, 10^15] &, 1, 20]

a(1) = 1; for n > 1, a(n) = 2851130928467*a(n-1) mod 10^15.

cp's OEIS Frontend

A384113 Consecutive states of a linear congruential pseudo-random number generator for MacModula-2 when started at 1.

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A384152 Consecutive states of the linear congruential pseudo-random number generator used by OMNITAB II when started at 1.

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A384361 Consecutive internal states of the linear congruential pseudo-random number generator of the HP 48 series calculators when started at 999500333083533.

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Author

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Programs

Mathematica

Formula

A384416 Consecutive internal states of the linear congruential pseudo-random number generator of the HP 48 series calculators when started at 1.

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Author

Keywords

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Crossrefs

Programs

Mathematica

Formula