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%I #20 Aug 01 2019 00:07:31
%S 1,2,3,4,5,6,8,9,10,12,13,15,16,18,20,21,24,25,26,27,30,32,34,39,40,
%T 42,45,48,50,52,55,63,64,65,68,72,75,78,80,84,89,102,104,105,110,117,
%U 120,125,126,128,130,136,144,165,168,169,170,178,189,192
%N Triple products of Fibonacci numbers: F(i)*F(j)*F(k), 2 <= i <= j <= k.
%C This sequence contains A049997 as a subsequence (aside from its first term), so a(n) << sqrt(phi)^n. All Fibonacci factors must be at most the number, so a(n) >> (phi^(1/3))^n. - _Charles R Greathouse IV_, Feb 06 2013
%H Charles R Greathouse IV, <a href="/A094563/b094563.txt">Table of n, a(n) for n = 1..10000</a>
%H C. Kimberling, <a href="http://www.fq.math.ca/Papers1/42-1/quartkimberling01_2004.pdf">Orderings of products of Fibonacci numbers</a>, Fibonacci Quart. 42:1 (2004), pp. 28-35.
%e F(2)*F(2)*F(2) = 1 < F(2)*F(2)*F(3) = 2 < ...
%e < F(4)*F(4)*F(4) = 27 < F(3)*F(4)*F(5) = 30 < F(3)*F(3)*F(6) = 32 < ...
%t Select[Union[Times@@@Tuples[Fibonacci[Range[12]],3]],#<200&] (* _Harvey P. Dale_, Dec 13 2011 *)
%o (PARI) list(lim)=my(phi=(1+sqrt(5))/2, v=vector(log(lim*sqrt(5))\log(phi),i,fibonacci(i+1)), u=List(), t, t1); for(i=1,#v, for(j=i,#v, t1=v[i]*v[j];if(t1>lim,break); for(k=j, #v, t=t1*v[k]; if(t>lim,break,listput(u,t))))); vecsort(Vec(u),,8) \\ _Charles R Greathouse IV_, Feb 06 2013
%Y Subsequence of A065108.
%Y Cf. A000045, A094564.
%K nonn
%O 1,2
%A _Clark Kimberling_, May 12 2004
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