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

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

Author

Moritz Franckenstein, Dec 16 2008

Keywords

• sign
• easy

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).

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Wikipedia, Linear congruential generator
• Index entries for sequences related to pseudo-random numbers.

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).