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A096553 Consecutive states of the linear congruential pseudo-random number generator used in function rand() in the Standard C library (VAX C) when started at 1.

%I A096553 #30 Jun 22 2025 18:20:46
%S A096553 1,1103527590,377401575,662824084,1147902781,2035015474,368800899,
%T A096553 1508029952,486256185,1062517886,267834847,180171308,836760821,
%U A096553 595337866,790425851,2111915288,1149758321,1644289366,1388290519,1647418052,1675546029
%N A096553 Consecutive states of the linear congruential pseudo-random number generator used in function rand() in the Standard C library (VAX C) when started at 1.
%C A096553 This is also the sequence of internal states of the generator described in Kernighan and Ritchie, which produces output limited to 15bit, see A061364. - A-number corrected by _Jean-Claude Arbaut_, Oct 05 2015
%D A096553 Brian W Kernighan and Dennis M. Ritchie, The C Programming Language (Second Edition) Prentice Hall Software Series, 1988.
%H A096553 Alois P. Heinz, <a href="/A096553/b096553.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harvey P. Dale)
%H A096553 B. D. Ripley, <a href="https://doi.org/10.1016/0377-0427(90)90346-2">Thoughts on pseudorandom number generators</a>, J of Computational and Applied Mathematics, 31, 1 (1990), 153-163.
%H A096553 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers.</a>
%F A096553 a(1)=1, a(n) = (1103515245 * a(n-1) + 12345) mod 2^31.
%p A096553 a:= proc(n) option remember; `if`(n<2, n,
%p A096553       irem(1103515245 *a(n-1)+12345, 2147483648))
%p A096553     end:
%p A096553 seq(a(n), n=1..30);  # _Alois P. Heinz_, Jun 10 2014
%t A096553 With[{c=2^31},NestList[Mod[1103515245#+12345,c]&,1,20]] (* _Harvey P. Dale_, Aug 01 2012 *)
%o A096553 (PARI) a(n) = if(n<2, 1, (1103515245 * a(n-1) + 12345) % (2^31));
%o A096553 vector(100, n, a(n)) \\ _Altug Alkan_, Oct 05 2015
%o A096553 (Magma) [n eq 1 select 1 else (1103515245 * Self(n-1) + 12345) mod (2^31): n in [1..25]]; // _Vincenzo Librandi_, Oct 06 2015
%Y A096553 Cf. A096550-A096561 (other pseudo-random number generators).
%K A096553 nonn
%O A096553 1,2
%A A096553 _Hugo Pfoertner_, Jul 18 2004