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A385079 Consecutive states of the linear congruential pseudo-random number generator 228*s mod (2^16+1) when started at s=1.

%I A385079 #19 Jun 20 2025 08:38:10
%S A385079 1,228,51984,55692,49135,61490,60339,60059,61756,55450,59496,64466,
%T A385079 17960,31586,58075,2626,8895,61950,34145,51694,55109,47285,32912,
%U A385079 32718,54023,61825,5645,41857,40531,351,14491,27098,17866,10154,21317,10538,43332,49146,63998
%N A385079 Consecutive states of the linear congruential pseudo-random number generator 228*s mod (2^16+1) when started at s=1.
%C A385079 Periodic with period 2^16.
%C A385079 Attributed by Sharp and Bays to L. Afflerbach.
%H A385079 Sean A. Irvine, <a href="/A385079/b385079.txt">Table of n, a(n) for n = 1..10000</a>
%H A385079 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 A385079 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers.</a>
%H A385079 <a href="/index/Rec#order_65536">Index entries for linear recurrences with constant coefficients</a>, order 65536.
%F A385079 a(n) = 228 * a(n-1) mod (2^16+1).
%p A385079 a:= proc(n) option remember; `if`(n<2, n,
%p A385079       irem(228*a(n-1), 65537))
%p A385079     end:
%p A385079 seq(a(n), n=1..44);  # after _Alois P. Heinz_
%t A385079 NestList[Mod[228*#, 65537] &, 1, 50] (* _Paolo Xausa_, Jun 17 2025 *)
%o A385079 (PARI) a(n) = lift(Mod(228, 65537)^(n-1)) \\ _Jianing Song_, Jun 17 2025
%Y A385079 Cf. A384113, A384971, A385002, A385080.
%K A385079 nonn,easy
%O A385079 1,2
%A A385079 _Sean A. Irvine_, Jun 16 2025