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A384610 Consecutive states of the linear congruential pseudo-random number generator (262145*s+3) mod 2^35 when started at s=1.

%I A384610 #11 Jun 12 2025 05:58:44
%S A384610 1,262148,1310727,3145738,5767181,9175056,13369363,18350102,24117273,
%T A384610 30670876,38010911,46137378,55050277,64749608,75235371,86507566,
%U A384610 98566193,111411252,125042743,139460666,154665021,170655808,187433027,204996678,223346761,242483276
%N A384610 Consecutive states of the linear congruential pseudo-random number generator (262145*s+3) mod 2^35 when started at s=1.
%C A384610 Periodic with period 2^35.
%D A384610 Donald E. Knuth, The Art of Computer Programming, Vol 2: Seminumerical Algorithms (3rd ed.), Addison-Wesley, 1998 (see p. 106).
%H A384610 Sean A. Irvine, <a href="/A384610/b384610.txt">Table of n, a(n) for n = 1..10000</a>
%H A384610 Martin Greenberger, <a href="https://doi.org/10.1145/321062.321065">Notes on a New Pseudo-Random Number Generator</a>, J ACM, 8, 2 (1961), 163-167.
%H A384610 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers</a>.
%F A384610 a(n) = (262145 * a(n-1) + 3) mod 2^35.
%p A384610 a:= proc(n) option remember; `if`(n<2, n,
%p A384610       irem(262145*a(n-1)+3, 2^35))
%p A384610     end:
%p A384610 seq(a(n), n=1..26);  # _Alois P. Heinz_, Jun 04 2025
%t A384610 NestList[Mod[262145*# + 3, 2^35] &, 1, 30] (* _Paolo Xausa_, Jun 12 2025 *)
%Y A384610 Cf. A384160, A384387, A384565, A384608.
%Y A384610 Cf. A096550-A096561 for other pseudo-random number generators.
%K A384610 nonn,easy
%O A384610 1,2
%A A384610 _Sean A. Irvine_, Jun 04 2025