OFFSET
1,3
COMMENTS
Starts the same as A049862, the product of two distinct Fibonacci numbers. This sequence has an infinite number of consecutive terms that are consecutive numbers (such as 15 and 16) because fib(k)*fib(k+3) and fib(k+1)*fib(k+2) differ by one for all k >= 0.
It follows from Carmichael's theorem that if u and v are finite sets of Fibonacci numbers such that (product of all the numbers in u) = (product of all the numbers in v), then u = v. The same holds for many other 2nd order linear recurrence sequences with constant coefficients. In the following guide to related "distinct product sequences", W = Wythoff array, A035513:
base sequence distinct-product sequence
row 2 of W: (4,7,11,...) A274286
row 3 of W: (6,10,16,...) A274287
row 4 of W: (9,15,24,...) A274288
- Clark Kimberling, Jun 17 2016
LINKS
T. D. Noe, Table of n, a(n) for n=1..1000
MATHEMATICA
s={1}; nn=30; f=Fibonacci[2+Range[nn]]; Do[s=Union[s, Select[s*f[[i]], #<=f[[nn]]&]], {i, nn}]; s=Prepend[s, 0]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 29 2009
STATUS
approved