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 1-3 of 3 results.

A152960 Output of linear congruential pseudo-random generator 134775813 for signed 32-bit values.

Original entry on oeis.org

0, 1, 134775814, -596792289, 870078620, 1172187917, -1410233534, 1368768587, 694906232, 1598751577, 1828254910, 352239543, 2039224980, 303092965, -683524998, 256513635, 1259699184, -355259471, 1580146294, -967806897, 1408429452, -1298476099, -669280590
Offset: 0

Views

Author

Moritz Franckenstein, Dec 16 2008

Keywords

Comments

A widely used pseudo-random number generator, for example all Delphi-Versions until now use it for their "Random" function.
It can be shown that the sequence has full period (its length is 2^32).

Crossrefs

Cf. A384404 (internal state).

Programs

  • Delphi
    // implementation using Delphi's built-in random() function
    var
    I: Integer;
    begin
    Randseed:= 0;
    for I:= 1 to 100 do begin
    Write(Randseed, ',');
    Random;
    end;
    end.
    
  • Mathematica
    nn=30; t = {x = 0}; Do[x = Mod[134775813 x + 1, 2^32]; If[x > 2^31, x = x - 2^32]; AppendTo[t, x], {nn}]; t (* T. D. Noe, Dec 18 2012 *)
  • PARI
    step(n)=(134775813*n+1)%2^32 \\ Charles R Greathouse IV, Sep 10 2015
    
  • PARI
    a(n)=lift((Mod(134775813,2^34)^n-1)/33693953)/4 \\ Charles R Greathouse IV, Sep 10 2015

Formula

a(n+1) = (134775813 * a(n) + 1) (mod 2^32) (representatives for the equivalence classes by interpreting the bit-patterns as two's complement).

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

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, May 27 2025

Keywords

Comments

Periodic with period 2^31-2.
Presented by Carta as an alternative to Park and Miller's Minimal Standard Generator.

Crossrefs

Programs

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

Formula

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

A385102 Consecutive internal states of the linear congruential pseudo-random number generator for Turbo Pascal 3.0 when started at 1.

Original entry on oeis.org

1, 907633514, 2028239699, 557549500, 4112042149, 3080093198, 3102664695, 1719420512, 3669547337, 1832837298, 1120443547, 3710930180, 2876256749, 2577566550, 2701236543, 1474796456, 2177815185, 2672918010, 2116672995, 3375510092, 2556738357, 14399646
Offset: 1

Views

Author

Sean A. Irvine, Jun 17 2025

Keywords

Crossrefs

Programs

  • Mathematica
    NestList[Mod[129# + 907633385, 2^32] &,1,21] (* Stefano Spezia, Jun 18 2025 *)

Formula

a(n) = (129 * a(n-1) + 907633385) mod 2^32.
Showing 1-3 of 3 results.