A384778 -id:A384778 - cp's OEIS frontend

A384696 Consecutive states of the linear congruential pseudo-random number generator Cray RANF when started at 1.

1, 44485709377909, 232253848878969, 94800993741645, 243522309605169, 20783065360997, 154093299791145, 161954398135485, 183663036741473, 207319719370837, 142356556532697, 278312552510253, 242082341486737, 37630394630981, 176334633251721, 233894773868189

Offset: 1

Sean A. Irvine, Jun 07 2025

Periodic with period 2^46.
Also implemented in the GNU Scientific Library as gsl_rng_ranf.
Also implemented in PASCLIB for Pascal programs on the CDC Cyber computers.

Sean A. Irvine, 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.
Mark Galassi, Jim Davies, James Theiler, Brian Gough, Gerard Jungman, Michael Booth, and Fabrice Rossi, GNU Scientific Library: Reference Manual, 2003 (see p. 181).
B. D. Ripley, Computer Generation of Random Variables: A Tutorial, International Statistical Review, 51 (1983), 301-309.
Index entries for sequences related to pseudo-random numbers.

Cf. A384746, A384775, A384776, A384778, A384779, A384780.
Cf. A384546, A384547, A384548, A384549, A384550, A384551, A384552
Cf. A096550-A096561 other pseudo-random number generators.

a:= proc(n) option remember; `if`(n<2, n,
      irem(44485709377909*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

NestList[Mod[44485709377909*#, 2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

a(n) = 44485709377909 * a(n-1) mod 2^48.

A384775 Consecutive states of the linear congruential pseudo-random number generator 33952834046453*s mod 2^48 when started at 1.

Original entry on oeis.org

1, 33952834046453, 181226512753785, 17547632994509, 138001340383537, 86153482263781, 229799995061289, 280681352600637, 119513974041441, 216025667693781, 238363414258905, 47318339740845, 113868956675729, 85138704755141, 217581192963721, 88846792569373

Offset: 1

Sean A. Irvine, Jun 09 2025

Periodic with period 2^46.

Sean A. Irvine, 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.
Index entries for sequences related to pseudo-random numbers.

Cf. A384696, A384746, A384776, A384778, A384779, A384780.

Cf. A384546, A384547, A384548, A384549, A384550, A384551, A384552.

a:= proc(n) option remember; `if`(n<2, n,
      irem(33952834046453*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

NestList[Mod[33952834046453*#, 2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

a(n) = 33952834046453 * a(n-1) mod 2^48.

A384776 Consecutive states of the linear congruential pseudo-random number generator 43272750451645*s mod 2^48 when started at 1.

Original entry on oeis.org

1, 43272750451645, 61318499813769, 79085427649829, 68025911569233, 83056068785613, 355731277657, 91085083377589, 166436801793953, 88719099065565, 111268338599465, 46775231680325, 152215507893489, 127293649213677, 121144755885561, 62037290331093

Offset: 1

Sean A. Irvine, Jun 09 2025

Periodic with period 2^46.

Sean A. Irvine, 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.
Index entries for sequences related to pseudo-random numbers.

Cf. A384696, A384746, A384775, A384778, A384779, A384780.

Cf. A384546, A384547, A384548, A384549, A384550, A384551, A384552.

a:= proc(n) option remember; `if`(n<2, n,
      irem(43272750451645*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

NestList[Mod[43272750451645*#,2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

a(n) = 43272750451645 * a(n-1) mod 2^48.

A384779 Consecutive states of the linear congruential pseudo-random number generator 68909602460261*s mod 2^48 when started at 1.

Original entry on oeis.org

1, 68909602460261, 267986871311321, 40223525715613, 170906480868849, 105934630117909, 220872133340233, 58531276790477, 54428804463841, 144397689558725, 44956117505465, 810057454589, 86145210100945, 204213264588917, 259238501435433, 238216607930925

Offset: 1

Sean A. Irvine, Jun 09 2025

Periodic with period 2^46.

Sean A. Irvine, 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.
Index entries for sequences related to pseudo-random numbers.

Cf. A384696, A384746, A384775, A384776, A384778, A384780.

Cf. A384546, A384547, A384548, A384549, A384550, A384551, A384552.

a:= proc(n) option remember; `if`(n<2, n,
      irem(68909602460261*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

NestList[Mod[68909602460261*#, 2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

a(n) = 68909602460261 * a(n-1) mod 2^48.

A384780 Consecutive states of the linear congruential pseudo-random number generator 127107890972165*s mod 2^48 when started at 1.

Original entry on oeis.org

1, 127107890972165, 97936613129241, 273514721657469, 208157768792689, 190871074753077, 130077535940873, 140242115373869, 12589906159073, 144775771571045, 83191635750649, 67018942496989, 27094905090641, 40503495991701, 211801672787433, 25600309900173

Offset: 1

Sean A. Irvine, Jun 09 2025

Periodic with period 2^46.

Sean A. Irvine, 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.
Index entries for sequences related to pseudo-random numbers.

Cf. A384696, A384746, A384775, A384776, A384778, A384779.

Cf. A384546, A384547, A384548, A384549, A384550, A384551, A384552.

a:= proc(n) option remember; `if`(n<2, n,
      irem(127107890972165*a(n-1), 2^48))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Jun 09 2025

NestList[Mod[127107890972165*#, 2^48] &, 1, 30] (* Paolo Xausa, Jun 11 2025 *)

a(n) = 127107890972165 * a(n-1) mod 2^48.

cp's OEIS Frontend

A384696 Consecutive states of the linear congruential pseudo-random number generator Cray RANF when started at 1.

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A384775 Consecutive states of the linear congruential pseudo-random number generator 33952834046453*s mod 2^48 when started at 1.

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A384776 Consecutive states of the linear congruential pseudo-random number generator 43272750451645*s mod 2^48 when started at 1.

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Maple

Mathematica

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A384779 Consecutive states of the linear congruential pseudo-random number generator 68909602460261*s mod 2^48 when started at 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A384780 Consecutive states of the linear congruential pseudo-random number generator 127107890972165*s mod 2^48 when started at 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula