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A384085 Consecutive states of the linear congruential pseudo-random number generator (40*s+725) mod 729 when started at s=1.

%I A384085 #20 May 28 2025 20:58:28
%S A384085 1,36,707,574,357,425,229,408,278,181,675,23,187,186,146,4,156,404,
%T A384085 118,342,554,286,501,353,265,390,287,541,495,113,142,573,317,283,381,
%U A384085 656,721,405,158,484,402,38,58,129,53,658,72,689,583,717,245,319,363,665
%N A384085 Consecutive states of the linear congruential pseudo-random number generator (40*s+725) mod 729 when started at s=1.
%C A384085 Periodic with period 729.
%C A384085 Originally defined by Savitch in the form (40*s+3641) mod 729, even though 3641 > 729.
%D A384085 Walter J. Savitch, Pascal: An Introduction to the Art and Science of Programming, Benjamin Cummings, 1984 (see p. 244).
%H A384085 Sean A. Irvine, <a href="/A384085/b384085.txt">Table of n, a(n) for n = 1..729</a>
%H A384085 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 A384085 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers</a>.
%H A384085 <a href="/index/Rec#order_729">Index entries for linear recurrences with constant coefficients</a>, order 729.
%F A384085 a(n) = (40*a(n-1) + 725) mod 729.
%p A384085 a:= proc(n) option remember; `if`(n<2, n,
%p A384085       irem(40*a(n-1)+725, 729))
%p A384085     end:
%p A384085 seq(a(n), n=1..54);  # _Alois P. Heinz_, May 18 2025
%t A384085 NestList[Mod[40*# + 725, 729] &, 1, 100] (* _Paolo Xausa_, May 22 2025 *)
%Y A384085 Cf. A096550-A096561 other pseudo-random number generators.
%K A384085 nonn,easy
%O A384085 1,2
%A A384085 _Sean A. Irvine_, May 18 2025