cp's OEIS Frontend

A384196 Consecutive states of the linear congruential pseudo-random number generator 20403*s mod 2^15 when started at s=1.

%I A384196 #17 Jul 06 2025 17:47:49
%S A384196 1,20403,30505,30891,9361,20579,16953,25819,6689,29715,1609,27659,
%T A384196 28849,27331,21337,15931,14401,25715,14697,2923,209,4387,18553,923,
%U A384196 23137,8403,4233,22219,21745,17283,8601,13563,129,10547,2985,20011,27921,483,24249,21083
%N A384196 Consecutive states of the linear congruential pseudo-random number generator 20403*s mod 2^15 when started at s=1.
%C A384196 Periodic with period 8192 (considerably smaller than the modulus).
%D A384196 Fred Maryanski, Digital Computer Simulation, Hayden Book Co., 1980 (see p. 224-230).
%H A384196 Sean A. Irvine, <a href="/A384196/b384196.txt">Table of n, a(n) for n = 1..8192</a>
%H A384196 Stephen K. Park and Keith W. Miller, <a href="https://doi.org/10.1145/63039.63042">Random number generators: good ones are hard to find</a>, Communications of the ACM, Vol 31, 10 (1988), 192-201.
%H A384196 W. E. Sharp and Carter Bays, <a href="https://doi.org/10.1016/0098-3004(92)90060-5">A review of portable random number generators</a>, Computers and Geosciences, 18, 1 (1982), 79-87.
%H A384196 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers</a>.
%H A384196 <a href="/index/Rec#order_8192">Index entries for linear recurrences with constant coefficients</a>, order 8192.
%F A384196 a(n) = 20403 * a(n-1) mod 2^15.
%p A384196 a:= proc(n) option remember; `if`(n<2, n,
%p A384196       irem(20403*a(n-1), 2^15))
%p A384196     end:
%p A384196 seq(a(n), n=1..40);  # _Alois P. Heinz_, May 21 2025
%t A384196 NestList[Mod[20403*#, 2^15] &, 1, 100] (* _Paolo Xausa_, May 22 2025 *)
%o A384196 (PARI) a(n) = lift(Mod(20403,32768)^(n-1)) \\ _Jianing Song_, Jul 06 2025
%Y A384196 Cf. A096550-A096561 (other pseudo-random number generators).
%K A384196 nonn,easy
%O A384196 1,2
%A A384196 _Sean A. Irvine_, May 21 2025