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A096560 Consecutive internal states of the first 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 A096560 #23 Aug 29 2024 11:58:03
%S A096560 2147483562,2147443549,546363367,801095798,1707599834,1415233705,
%T A096560 19915560,184815967,1440196129,286492701,451678520,242633072,
%U A096560 2094038248,332794338,2034550132,1534592081,22528712,1668269071,1739534702,1504321872,2118598881,1701974909,1825258870
%N A096560 Consecutive internal states of the first 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 A096560 Comment from _Raymond Wang_, Oct 03 2008: (65421664*40014) mod (2^31-85) = 2^31-86.
%D A096560 P. L'Ecuyer, Efficient and portable combined random number generators, Communications of the ACM, v.31 n.6, p. 742-751 and 774, 1988.
%H A096560 Alois P. Heinz, <a href="/A096560/b096560.txt">Table of n, a(n) for n = 1..10000</a>
%H A096560 P. L'Ecuyer, <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/handsim.ps">Random Number Generation</a>, Chapter 4 of the Handbook on Simulation, Jerry Banks Ed., Wiley, 1998.
%H A096560 <a href="https://software.intel.com/sites/default/files/m/d/4/1/d/8/for_lang.pdf">Intel FORTRAN Language Reference</a>, Document No. 253261-002, Chapter 9, Intrinsic Procedure RANDOM_NUMBER.
%H A096560 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers</a>.
%F A096560 a(1)=2^31-86, a(n)=40014*a(n-1) mod (2^31-85).
%p A096560 a:= proc(n) option remember; `if`(n=1, 2147483562,
%p A096560       irem(40014 *a(n-1), 2147483563))
%p A096560     end:
%p A096560 seq(a(n), n=1..30);  # _Alois P. Heinz_, Jun 10 2014
%t A096560 NestList[Mod[#*40014, 2^31 - 85] &, 2^31 - 86, 50] (* _Paolo Xausa_, Aug 29 2024 *)
%Y A096560 Cf. A096561.
%K A096560 nonn
%O A096560 1,1
%A A096560 _Hugo Pfoertner_, Aug 13 2004