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A384961 Consecutive states of the linear congruential pseudo-random number generator (257*s + 41) mod 2^16 when started at s=1.

%I A384961 #14 Jun 18 2025 12:20:52
%S A384961 1,298,11091,32380,64165,40910,28151,25888,34121,52850,16539,56260,
%T A384961 40941,36118,41791,57960,19089,56250,38371,30988,34101,47710,6279,
%U A384961 40880,20441,10498,11051,22100,43645,10150,52687,40184,38177,46666,115,29596,4037,54510
%N A384961 Consecutive states of the linear congruential pseudo-random number generator (257*s + 41) mod 2^16 when started at s=1.
%C A384961 Periodic with period 2^16.
%H A384961 Sean A. Irvine, <a href="/A384961/b384961.txt">Table of n, a(n) for n = 1..10000</a>
%H A384961 B. D. Ripley, <a href="https://doi.org/10.2307/1402590">Computer Generation of Random Variables: A Tutorial</a>, International Statistical Review, 51 (1983), 301-309.
%H A384961 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 A384961 Alan Tootill, <a href="https://archive.org/details/PersonalComputerWorld1982-02/page/156/mode/2up">PCW Subset</a>, Personal Computer World, Feb 1982 (see p. 157).
%H A384961 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers.</a>
%H A384961 <a href="/index/Rec#order_65536">Index entries for linear recurrences with constant coefficients</a>, order 65536.
%F A384961 a(n) = (257 * a(n-1) + 41) mod 2^16.
%p A384961 a:= proc(n) option remember; `if`(n<2, n,
%p A384961       irem(257*a(n-1)+41, 2^16))
%p A384961     end:
%p A384961 seq(a(n), n=1..38);  # _Alois P. Heinz_, Jun 13 2025
%t A384961 NestList[Mod[257*# + 41, 2^16] &, 1, 50] (* _Paolo Xausa_, Jun 18 2025 *)
%Y A384961 Cf. A357907, A384934, A384935.
%K A384961 nonn,easy
%O A384961 1,2
%A A384961 _Sean A. Irvine_, Jun 13 2025