A271356 -id:A271356 - cp's OEIS frontend

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

6, 10, 15, 16, 24, 26, 39, 40, 42, 63, 65, 68, 102, 104, 105, 110, 165, 168, 170, 178, 267, 272, 273, 275, 288, 432, 440, 442, 445, 466, 699, 712, 714, 715, 720, 754, 1131, 1152, 1155, 1157, 1165, 1220, 1830, 1864, 1869, 1870, 1872, 1885, 1974, 2961, 3016

Offset: 1

Clark Kimberling, May 02 2016

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).

			2*3 = 6, 2*5 = 10, 3*5 = 15, 2*8 = 16.

Clark Kimberling, Table of n, a(n) for n = 1..1000
Clark Kimberling, Orderings of products of Fibonacci numbers, Fibonacci Quarterly 42:1 (2004), pp. 28-35.

Cf. A000045, A004526, A094565, A271356 (difference sequence), subsequence of A049997.

z = 200; f[n_] := Fibonacci[n];
Take[Sort[Flatten[Table[f[m] f[n], {n, 3, z}, {m, 3, n - 1}]]], 100]
Times@@@Subsets[Fibonacci[Range[3,20]],{2}]//Union (* Harvey P. Dale, Jul 12 2025 *)

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

A004526(n) = number of numbers a(k) between F(n+3) and F(n+4), where F = A000045 (Fibonacci numbers).

cp's OEIS Frontend

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

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