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A385039 Consecutive internal states of the linear congruential pseudo-random number generator (171*s + 11213) mod 53125 when started at 1.

%I A385039 #13 Jun 24 2025 09:59:02
%S A385039 1,11384,45377,14430,34993,45016,5824,50867,50095,24333,28406,34264,
%T A385039 26607,45385,15798,3296,43579,25722,300,9388,22811,33769,48212,21090,
%U A385039 5103,33826,4834,40952,1505,2943,36341,9899,3942,47795,2908,30356,48964,43432,585,4998
%N A385039 Consecutive internal states of the linear congruential pseudo-random number generator (171*s + 11213) mod 53125 when started at 1.
%C A385039 Periodic with period 53125.
%C A385039 Described in Numerical Recipes as a "quick and dirty" generator.
%D A385039 William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).
%H A385039 Sean A. Irvine, <a href="/A385039/b385039.txt">Table of n, a(n) for n = 1..10000</a>
%H A385039 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 A385039 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers.</a>
%H A385039 <a href="/index/Rec#order_53125">Index entries for linear recurrences with constant coefficients</a>, order 53125.
%F A385039 a(n) = (171*a(n-1) + 11213) mod 53125.
%p A385039 a:= proc(n) option remember; `if`(n<2, n,
%p A385039       irem(171*a(n-1)+11213, 53125))
%p A385039     end:
%p A385039 seq(a(n), n=1..45);  # after _Alois P. Heinz_
%t A385039 NestList[Mod[171*# + 11213, 53125] &, 1, 50] (* _Paolo Xausa_, Jun 16 2025 *)
%Y A385039 Cf. A384113, A384114, A384126, A384152, A384158, A384196.
%K A385039 nonn,easy
%O A385039 1,2
%A A385039 _Sean A. Irvine_, Jun 13 2025