login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A271354 Products of two distinct Fibonacci numbers, both greater than 1. 10
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 (list; graph; refs; listen; history; text; internal format)
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: A095678 A151972 A094564 * A315240 A315241 A166160

Adjacent sequences:  A271351 A271352 A271353 * A271355 A271356 A271357

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 02 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)