A096558 -id:A096558 - cp's OEIS frontend

A061364 Pseudo-random numbers: a (very weak) pseudo-random number generator from the second edition of the C book.

16838, 5758, 10113, 17515, 31051, 5627, 23010, 7419, 16212, 4086, 2749, 12767, 9084, 12060, 32225, 17543, 25089, 21183, 25137, 25566, 26966, 4978, 20495, 10311, 11367, 30054, 17031, 13145, 19882, 25736, 30524, 28505, 28394

Offset: 0

Frank Ellermann, Jun 11 2001

WATCOM C/C++ 10.0b uses this sequence for stdlib.h rand(). MS C 6.0 and gcc 2.6.3 use other (similar) sequences.

Brian W. Kernighan and Dennis M. Ritchie, The C Programming Language, Second Edition, ANSI C, 1988, Prentice-Hall Internat., ch. 2.7.
Brian W. Kernighan and Dennis M. Ritchie, The C-programming-language [German], 1990, Hanser, p. 45.

Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for sequences related to pseudo-random numbers.

Cf. A096558, A221555, A221556, A221557, A221558, A221559, A221560, A221561, A221562, A260083.

A096554 is the same sequence seeded with 0.

unsigned long next= 1; int i= 0; while (i++ < 33) next= next * 1103515245 + 12345, printf( "%d ", (unsigned)( next/65536 ) %32768 );

x=1; m=2^32; for (n=0, 1000, x=(x*1103515245 + 12345)%m; write("b061364.txt", n, " ", (x\65536)%32768) ) \\ Harry J. Smith, Jul 21 2009

From David Fifield, May 23 2024: (Start)
a(n) = A096554(n+934703610).
a(n) = floor(A096553(n+2)/65536) mod 32768. (End)

A035331 Base-1000 expansion of Pi.

Original entry on oeis.org

3, 141, 592, 653, 589, 793, 238, 462, 643, 383, 279, 502, 884, 197, 169, 399, 375, 105, 820, 974, 944, 592, 307, 816, 406, 286, 208, 998, 628, 34, 825, 342, 117, 67, 982, 148, 86, 513, 282, 306, 647, 93, 844, 609, 550, 582, 231, 725, 359, 408, 128, 481, 117, 450

Offset: 0

Jörg Zurkirchen

Start with a(0)=3; other terms are formed from triples of successive digits in the decimal expansion of Pi.

This sequence can be considered as a (pseudo)random generator with range 0..999. Its scatterplot graph is very similar to that of other random generators, e.g., A096558. - M. F. Hasler, May 14 2015

			Pi = 3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 ...

T. D. Noe, Table of n, a(n) for n = 0..10000

Cf. A000796, A016062, A037244, A050819, A032445, A064467.

RealDigits[Pi,1000,60][[1]] (* Harvey P. Dale, Nov 22 2015 *)

default(realprecision,3*N=100);vector(N,i,Pi\1000^(1-i)%1000) \\ or: {P=Pi;vector(N,i,P\1+0*P=frac(P)*1000)} or {P=Pi/1000;vector(N,i,floor(P=frac(P)*1000))}. \\ M. F. Hasler, May 11 2015

a(n) = floor(Pi*10^(3n)) mod 1000. - M. F. Hasler, May 14 2015

More terms from Larry Reeves (larryr(AT)acm.org), Oct 04 2001

Better definition from Franklin T. Adams-Watters, Apr 10 2006

A096557 Consecutive internal states of the linear congruential pseudo-random number generator rand() used in Microsoft's Visual C++.

Original entry on oeis.org

0, 2531011, 505908858, 3539360597, 159719620, 2727824503, 773150046, 548247209, 2115878600, 2832368235, 2006221698, 2531105853, 3989110284, 2222380191, 2165923046, 1345953809, 1043415696, 586225427, 3870123402, 2343900709, 3109564500, 3522190791, 2090033518, 3566711417

Offset: 1

Hugo Pfoertner, Jul 21 2004

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index entries for sequences related to pseudo-random numbers.

Cf. A096558 corresponding output. A096550-A096561 other pseudo-random number generators.

a:= proc(n) option remember; `if`(n<2, 0,
      irem(214013 *a(n-1) +2531011, 4294967296))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 10 2014

NestList[Mod[#*214013 + 2531011, 2^32] &, 0, 50] (* Paolo Xausa, Aug 29 2024 *)

A096557(n)=lift((Mod(214013,2^34)^(n-1)-1)*13129821757)>>2 \\ M. F. Hasler, May 14 2015

a(1)=0, a(n)=(a(n-1) * 214013 + 2531011) mod 2^32. The sequence is periodic with period length 2^32.

A260083 Consecutive numbers generated by the 'random' function in PARI (32 bit, version > 2.4) using the default argument (2^31).

Original entry on oeis.org

326511477, 1362174608, 903267448, 656347688, 1853455872, 693790135, 1743812782, 1381849689, 1919384312, 561030593, 610902088, 1730365257, 1381380589, 1437333698, 1880143150, 1861285526, 135271255, 2062787134, 476812016, 748713098, 702275007, 1351923632

Offset: 1

Felix Fröhlich, Jul 15 2015

nonn

These are the values the function generates in PARI/GP v 2.7.0, using Richard Brent's XORGEN algorithm.
For all n, 0 < a(n) < 2^31.
All 32-bit PARI versions > 2.4 should yield this sequence of pseudo-random numbers, when the random generator is in its initial state or reset to that state using setrand(1). - M. F. Hasler, Sep 18 2016
The generator has a period of 2^4096-1. - Hugo Pfoertner, Sep 18 2016

Felix Fröhlich, Table of n, a(n) for n = 1..10000
Richard P. Brent, Some long-period random number generators using shifts and xors, ANZIAM Journal 48 (CTAC2006), C188-C202, 2007.
PARI, Catalogue of GP/PARI Functions, Conversions and similar elementary functions or commands: random({N = 2^{{31}}})
Index entries for sequences related to pseudo-random numbers.

Cf. A061364, A096558, A221555, A221556, A221557, A221558, A221559, A221560, A221561, A221562.

Cf. A276820: Corresponding 64 bit random number generator.

a(n) = random \\ Works only if called first with n=1, then with n=2, etc, and if the internal random generator was never called before or reset via setrand(1)

setrand(1); A260083=vector(100,i,random()) \\ M. F. Hasler, Sep 18 2016

A084275 Pseudo-random numbers: MS C 6.0 version.

Original entry on oeis.org

41, 18467, 6334, 26500, 19169, 15724, 11478, 29358, 26962, 24464, 5705, 28145, 23281, 16827, 9961, 491, 2995, 11942, 4827, 5436, 32391, 14604, 3902, 153, 292, 12382, 17421, 18716, 19718, 19895, 5447, 21726, 14771

Offset: 0

Frank Ellermann, May 20 2003

Zhuorui He, Table of n, a(n) for n = 0..10000 (terms 0..98 from Alan Klette).
Sean A. Irvine, Java program (github)
Index entries for sequences related to pseudo-random numbers.

Cf. A084276, A084277, A096557, A096558, A061364, A384289.

#include 
int main()
{
    long next = 1;
    int i = 0;
    while ( i++ < 33 )
    {
        next = next * 214013L + 2531011L;
        printf( "%d ", (unsigned)( next >> 16) & 0x7FFF );
    }
    printf("\n");
    return 0;
}

a(n) = A096558(n+199670977) = floor((A096557(n+199670977) mod 2^31)/2^16). - Zhuorui He, Aug 22 2025

Corrected by Alan Klette, Jun 09 2019

cp's OEIS Frontend

A061364 Pseudo-random numbers: a (very weak) pseudo-random number generator from the second edition of the C book.

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A035331 Base-1000 expansion of Pi.

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A096557 Consecutive internal states of the linear congruential pseudo-random number generator rand() used in Microsoft's Visual C++.

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Maple

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A260083 Consecutive numbers generated by the 'random' function in PARI (32 bit, version > 2.4) using the default argument (2^31).

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PARI

PARI

A084275 Pseudo-random numbers: MS C 6.0 version.

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C

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