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A271354 Products of two distinct Fibonacci numbers, both greater than 1.

%I A271354 #14 Jul 12 2025 11:14:31
%S A271354 6,10,15,16,24,26,39,40,42,63,65,68,102,104,105,110,165,168,170,178,
%T A271354 267,272,273,275,288,432,440,442,445,466,699,712,714,715,720,754,1131,
%U A271354 1152,1155,1157,1165,1220,1830,1864,1869,1870,1872,1885,1974,2961,3016
%N A271354 Products of two distinct Fibonacci numbers, both greater than 1.
%C A271354 For n > 5, the numbers F(i)*F(j) satisfying F(n-1) <= F(i)*F(j) <= F(n) also satisfy F(n-1) < F(i)*F(j) < F(n).  They are the numbers for which i + j = n + 1, where 2 < i < j, so that the number of such F(i)*F(j) is floor(n/2) - 2.  The least is 3*F(n-3) and the greatest is 2*F(n-2).
%H A271354 Clark Kimberling, <a href="/A271354/b271354.txt">Table of n, a(n) for n = 1..1000</a>
%H A271354 Clark Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/42-1/quartkimberling01_2004.pdf">Orderings of products of Fibonacci numbers</a>, Fibonacci Quarterly 42:1 (2004), pp. 28-35.
%F A271354 A004526(n) = number of numbers a(k) between F(n+3) and F(n+4), where F = A000045 (Fibonacci numbers).
%e A271354 2*3 = 6, 2*5 = 10, 3*5 = 15, 2*8 = 16.
%t A271354 z = 200; f[n_] := Fibonacci[n];
%t A271354 Take[Sort[Flatten[Table[f[m] f[n], {n, 3, z}, {m, 3, n - 1}]]], 100]
%t A271354 Times@@@Subsets[Fibonacci[Range[3,20]],{2}]//Union (* _Harvey P. Dale_, Jul 12 2025 *)
%o A271354 (PARI) list(lim)=my(v=List,F=vector(A130233(lim\2),k,fibonacci(k)),t); for(i=2,#F, for(j=1,i-1, t=F[i]*F[j]; if(t>lim,break); listput(v,t))); Set(v) \\ _Charles R Greathouse IV_, Oct 07 2016
%Y A271354 Cf. A000045, A004526, A094565, A271356 (difference sequence), subsequence of A049997.
%K A271354 nonn,easy
%O A271354 1,1
%A A271354 _Clark Kimberling_, May 02 2016