cp's OEIS Frontend

A385080 Consecutive states of the linear congruential pseudo-random number generator 237*s mod (2^16+1) when started at s=1.

%I A385080 #17 Jun 20 2025 08:21:54
%S A385080 1,237,56169,8042,5381,30094,54282,19582,53344,59424,58570,52783,
%T A385080 57541,5521,63274,53502,31333,20240,12679,55758,41709,54483,1682,5412,
%U A385080 37441,26022,6736,23544,9283,37350,4455,7243,12629,43908,51350,45605,60317,8063,10358
%N A385080 Consecutive states of the linear congruential pseudo-random number generator 237*s mod (2^16+1) when started at s=1.
%C A385080 Periodic with period 2^16.
%C A385080 Attributed by Sharp and Bays to L. Afflerbach.
%H A385080 Sean A. Irvine, <a href="/A385080/b385080.txt">Table of n, a(n) for n = 1..10000</a>
%H A385080 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 A385080 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers.</a>
%H A385080 <a href="/index/Rec#order_65536">Index entries for linear recurrences with constant coefficients</a>, order 65536.
%F A385080 a(n) = 237 * a(n-1) mod (2^16+1).
%p A385080 a:= proc(n) option remember; `if`(n<2, n,
%p A385080       irem(237*a(n-1), 65537))
%p A385080     end:
%p A385080 seq(a(n), n=1..44);  # after _Alois P. Heinz_
%t A385080 NestList[Mod[237*#, 65537] &, 1, 50] (* _Paolo Xausa_, Jun 17 2025 *)
%o A385080 (PARI) a(n) = lift(Mod(237,65537)^(n-1)) \\ _Jianing Song_, Jun 17 2025
%Y A385080 Cf. A385079.
%K A385080 nonn,easy
%O A385080 1,2
%A A385080 _Sean A. Irvine_, Jun 16 2025