A094563 Triple products of Fibonacci numbers: F(i)*F(j)*F(k), 2 <= i <= j <= k.

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, 42, 45, 48, 50, 52, 55, 63, 64, 65, 68, 72, 75, 78, 80, 84, 89, 102, 104, 105, 110, 117, 120, 125, 126, 128, 130, 136, 144, 165, 168, 169, 170, 178, 189, 192

Offset

1,2

Comments

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

C. Kimberling, Orderings of products of Fibonacci numbers, Fibonacci Quart. 42:1 (2004), pp. 28-35.

Example

F(2)*F(2)*F(2) = 1 < F(2)*F(2)*F(3) = 2 < ...
< F(4)*F(4)*F(4) = 27 < F(3)*F(4)*F(5) = 30 < F(3)*F(3)*F(6) = 32 < ...

Mathematica

Select[Union[Times@@@Tuples[Fibonacci[Range[12]], 3]], #<200&] (* Harvey P. Dale, Dec 13 2011 *)

Prog

(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

Crossrefs

Subsequence of A065108.

Cf. A000045, A094564.

Sequence in context: A245030 A245027 A065108 * A228897 A068095 A064390

Adjacent sequences: A094560 A094561 A094562 * A094564 A094565 A094566

Keyword

nonn

Author

Clark Kimberling, May 12 2004

Status

approved