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

1,1

Comments

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).

Links

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.

Formula

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

Example

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

Mathematica

z = 200; f[n_] := Fibonacci[n];
Take[Sort[Flatten[Table[f[m] f[n], {n, 3, z}, {m, 3, n - 1}]]], 100]

Prog

(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

Crossrefs

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

Sequence in context: A339116 A151972 A094564 * A315240 A315241 A166160

Adjacent sequences: A271351 A271352 A271353 * A271355 A271356 A271357

Keyword

nonn,easy

Author

Clark Kimberling, May 02 2016

Status

approved