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A384194 Consecutive states of the linear congruential pseudo-random number generator 259*s mod 2^15 when started at s=1.

%I A384194 #19 Jun 15 2025 22:36:22
%S A384194 1,259,1545,6939,27729,5619,13529,30603,29089,30179,17577,30459,24561,
%T A384194 4307,1401,2411,1857,22211,18249,7899,14225,14259,23065,10059,16609,
%U A384194 9123,3561,4795,29489,2707,12985,20779,7809,23683,6281,21147,4817,2419,3929,1803,8225
%N A384194 Consecutive states of the linear congruential pseudo-random number generator 259*s mod 2^15 when started at s=1.
%C A384194 Periodic with period 8192 (considerably less than the modulus).
%C A384194 A 16-bit version of RANDU (A096555) that suffers from all the same problems.
%D A384194 Byron S. Gottfried, Schaum's Outline of Theory and Problems of Programming with Pascal, McGraw-Hill, 1985 (see p. 143).
%H A384194 Sean A. Irvine, <a href="/A384194/b384194.txt">Table of n, a(n) for n = 1..8192</a>
%H A384194 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 A384194 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 A384194 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers</a>.
%F A384194 a(n) = 259 * a(n-1) mod 2^15.
%p A384194 a:= proc(n) option remember; `if`(n<2, n,
%p A384194       irem(259*a(n-1), 2^15))
%p A384194     end:
%p A384194 seq(a(n), n=1..41);  # _Alois P. Heinz_, May 21 2025
%t A384194 NestList[Mod[259*#, 2^15] &, 1, 100] (* _Paolo Xausa_, May 22 2025 *)
%Y A384194 Cf. A096555, A384158.
%K A384194 nonn,easy
%O A384194 1,2
%A A384194 _Sean A. Irvine_, May 21 2025