cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A384971 Consecutive internal states of the linear congruential pseudo-random number generator (106*s + 1283) mod 6075 when started at 1.

Original entry on oeis.org

1, 1389, 2717, 3760, 4968, 5441, 904, 5982, 3575, 3583, 4431, 3194, 5722, 315, 4298, 1246, 5784, 812, 2305, 2613, 4886, 2824, 2952, 4370, 2803, 726, 5339, 2242, 2010, 1718, 1141, 729, 5657, 5575, 2958, 5006, 3394, 2622, 5840, 673, 5796, 2084, 3487, 330, 5888
Offset: 1

Views

Author

Sean A. Irvine, Jun 13 2025

Keywords

Comments

Periodic with period 6075.
Described in Numerical Recipes as a "quick and dirty" generator.

References

  • William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Links

Crossrefs

Cf. A384113, A384114, A384126, A384152, A384158, A384196.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n<2, n,
      irem(106*a(n-1)+1283, 6075))
    end:
seq(a(n), n=1..45);  # Alois P. Heinz, Jun 13 2025
  • Mathematica
    NestList[Mod[106*# + 1283, 6075] &, 1, 50] (* Paolo Xausa, Jun 17 2025 *)

Formula

a(n) = (106*a(n-1) + 1283) mod 6075.

A384160 Consecutive states of the linear congruential pseudo-random number generator for 36-bit WATFOR/WATFIV when started at 1.

Original entry on oeis.org

1, 131069, 17179082761, 17183408101, 34345582673, 53083917, 16988766937, 17848727413, 32066509217, 7739650845, 25740764841, 33596591109, 30610037745, 12186659885, 12166953849, 6296898965, 7334844225, 19577928253, 5497393481, 14152584229, 20226775953
Offset: 1

Views

Author

Sean A. Irvine, May 20 2025

Keywords

Comments

Periodic with period 2^33 (considerably less than the modulus).
WATFOR and WATFIV are early FORTRAN compilers from the University of Waterloo.

References

  • Terry M. Walker, Fundamentals of Fortran Programming: with WATFOR/WATFIV, Allyn and Bacon, 1975.

Links

Crossrefs

Cf. A384158, A384159.
Cf. A096550-A096561 other pseudo-random number generators.

Programs

  • Mathematica
    NestList[Mod[131069*#, 2^35] &, 1, 20] (* Stefano Spezia, May 24 2025 *)

Formula

a(n) = 131069 * a(n-1) mod 2^35.

A384194 Consecutive states of the linear congruential pseudo-random number generator 259*s mod 2^15 when started at s=1.

Original entry on oeis.org

1, 259, 1545, 6939, 27729, 5619, 13529, 30603, 29089, 30179, 17577, 30459, 24561, 4307, 1401, 2411, 1857, 22211, 18249, 7899, 14225, 14259, 23065, 10059, 16609, 9123, 3561, 4795, 29489, 2707, 12985, 20779, 7809, 23683, 6281, 21147, 4817, 2419, 3929, 1803, 8225
Offset: 1

Views

Author

Sean A. Irvine, May 21 2025

Keywords

Comments

Periodic with period 8192 (considerably less than the modulus).
A 16-bit version of RANDU (A096555) that suffers from all the same problems.

References

  • Byron S. Gottfried, Schaum's Outline of Theory and Problems of Programming with Pascal, McGraw-Hill, 1985 (see p. 143).

Links

Crossrefs

Cf. A096555, A384158.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n<2, n,
      irem(259*a(n-1), 2^15))
    end:
seq(a(n), n=1..41);  # Alois P. Heinz, May 21 2025
  • Mathematica
    NestList[Mod[259*#, 2^15] &, 1, 100] (* Paolo Xausa, May 22 2025 *)

Formula

a(n) = 259 * a(n-1) mod 2^15.

A385039 Consecutive internal states of the linear congruential pseudo-random number generator (171*s + 11213) mod 53125 when started at 1.

Original entry on oeis.org

1, 11384, 45377, 14430, 34993, 45016, 5824, 50867, 50095, 24333, 28406, 34264, 26607, 45385, 15798, 3296, 43579, 25722, 300, 9388, 22811, 33769, 48212, 21090, 5103, 33826, 4834, 40952, 1505, 2943, 36341, 9899, 3942, 47795, 2908, 30356, 48964, 43432, 585, 4998
Offset: 1

Views

Author

Sean A. Irvine, Jun 13 2025

Keywords

Comments

Periodic with period 53125.
Described in Numerical Recipes as a "quick and dirty" generator.

References

  • William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Links

Crossrefs

Cf. A384113, A384114, A384126, A384152, A384158, A384196.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n<2, n,
      irem(171*a(n-1)+11213, 53125))
    end:
seq(a(n), n=1..45);  # after Alois P. Heinz
  • Mathematica
    NestList[Mod[171*# + 11213, 53125] &, 1, 50] (* Paolo Xausa, Jun 16 2025 *)

Formula

a(n) = (171*a(n-1) + 11213) mod 53125.

A384159 Consecutive states of the linear congruential pseudo-random number generator for 32-bit WATFOR/WATFIV when started at 1.

Original entry on oeis.org

1, 20613, 424895769, 938169853, 404929649, 1693398709, 828374025, 631292077, 1220159969, 1976439269, 430365689, 2020481117, 2026879057, 763630101, 1799615721, 1993805069, 1909315521, 1935501125, 533477081, 1446792893, 636483633, 859521397, 574460361, 126586221
Offset: 1

Views

Author

Sean A. Irvine, May 20 2025

Keywords

Comments

Periodic with period 2^29 (considerably less than the modulus).
WATFOR and WATFIV are early FORTRAN compilers from the University of Waterloo.

References

  • Terry M. Walker, Fundamentals of Fortran Programming: with WATFOR/WATFIV, Allyn and Bacon, 1975.

Links

Crossrefs

Cf. A384158, A384160.
Cf. A096550-A096561 other pseudo-random number generators.

Programs

  • Mathematica
    NestList[Mod[20613*#, 2^31] &, 1, 23] (* Stefano Spezia, May 24 2025 *)

Formula

a(n) = 20613 * a(n-1) mod 2^31.

A384973 Consecutive states of the linear congruential pseudo-random number generator (101*s+1) mod 2^13 when started at s=1.

Original entry on oeis.org

1, 102, 2111, 220, 5837, 7906, 3883, 7160, 2265, 7582, 3927, 3412, 549, 6298, 5315, 4336, 3761, 3030, 2927, 716, 6781, 4946, 8027, 7912, 4489, 2830, 7303, 324, 8149, 3850, 3827, 1504, 4449, 6982, 671, 2236, 4653, 3010, 907, 1496, 3641, 7294, 7607, 6452, 4485
Offset: 1

Views

Author

Sean A. Irvine, Jun 13 2025

Keywords

Comments

Periodic with period 2^13.

Links

Crossrefs

Cf. A384126, A384152, A384158, A384194.

Programs

  • Mathematica
    NestList[Mod[101*# + 1, 2^13] &, 1, 50] (* Paolo Xausa, Jun 18 2025 *)

Formula

a(n) = (101*a(n-1) + 1) mod 2^13.

A385038 Consecutive internal states of the linear congruential pseudo-random number generator (1366*s + 1283) mod 6075 when started at 1.

Original entry on oeis.org

1, 2649, 5192, 4030, 2313, 1841, 1039, 5082, 5645, 3178, 4881, 4454, 4372, 1710, 4343, 4621, 1644, 5312, 3925, 4683, 1286, 2284, 4752, 4415, 5773, 1851, 2549, 2242, 2055, 1763, 3841, 5364, 2057, 4495, 5703, 3431, 4204, 3072, 5885, 2968, 3546, 3344, 787, 1050
Offset: 1

Views

Author

Sean A. Irvine, Jun 13 2025

Keywords

Comments

Periodic with period 6075.
Described in Numerical Recipes as a "quick and dirty" generator.

References

  • William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Links

Crossrefs

Cf. A384113, A384114, A384126, A384152, A384158, A384196, A384971, A385037.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n<2, n,
      irem(1366*a(n-1)+1283, 6075))
    end:
seq(a(n), n=1..45);  # after Alois P. Heinz
  • Mathematica
    NestList[Mod[1366*# + 1283, 6075] &, 1, 50] (* Paolo Xausa, Jun 16 2025 *)

Formula

a(n) = (1366*a(n-1) + 1283) mod 6075.
Showing 1-7 of 7 results.

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