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A096561 Consecutive internal states of the second of the two linear congruential random number generators whose combined output is used in function RANDOM_NUMBER in version 8 of the Intel FORTRAN Compiler for Linux, using its intrinsic initialization.

%I A096561 #30 May 29 2025 06:08:12
%S A096561 2147483398,2147442707,491644535,44073136,275411947,1494571342,
%T A096561 367188984,1612130085,1622029567,724872099,810967243,1649143122,
%U A096561 223185073,139696145,126975187,29251410,592572674,1023646436,1632766708,1701483674,1908878648,1615402586,1642669521
%N A096561 Consecutive internal states of the second of the two linear congruential random number generators whose combined output is used in function RANDOM_NUMBER in version 8 of the Intel FORTRAN Compiler for Linux, using its intrinsic initialization.
%C A096561 This is part 2 of a combined pseudorandom number generator proposed by Pierre L'Ecuyer. For more information, references and links see A096560. For the spectral properties see Table 1, line 21, on page 106 of Knuth's TAOCP Vol. 2.
%C A096561 This sequence has period 2^31 - 250. - _Charles R Greathouse IV_, Sep 10 2015
%D A096561 D. E. Knuth, The Art of Computer Programming Third Edition. Vol. 2 Seminumerical Algorithms. Chapter 3.3.4 The Spectral Test, Page 108. Addison-Wesley 1997.
%H A096561 Alois P. Heinz, <a href="/A096561/b096561.txt">Table of n, a(n) for n = 1..10000</a>
%H A096561 Pierre L'Ecuyer, <a href="https://doi.org/10.1145/62959.62969">Efficient and portable combined random number generators</a>, Commun. ACM, 31, 6 (1988), 742-749 and 774.
%H A096561 <a href="/index/Per#periodic">Index entries for periodic sequences with large period</a>.
%H A096561 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers</a>.
%F A096561 a(1)=2^31-250, a(n)=40692*a(n-1) mod (2^31-249).
%p A096561 a:= proc(n) option remember; `if`(n=1, 2147483398,
%p A096561       irem(40692 *a(n-1), 2147483399))
%p A096561     end:
%p A096561 seq(a(n), n=1..30);  # _Alois P. Heinz_, Jun 10 2014
%t A096561 NestList[Mod[#*40692, 2^31 - 249] &, 2^31 - 250, 50] (* _Paolo Xausa_, Aug 29 2024 *)
%o A096561 (PARI) a(n)=lift(-Mod(40692,2147483399)^(n-1)) \\ _M. F. Hasler_, May 14 2015
%Y A096561 Cf. A096550-A096560, A061364.
%K A096561 nonn,easy
%O A096561 1,1
%A A096561 _Hugo Pfoertner_, Aug 13 2004