OFFSET
1,3
COMMENTS
There are no duplicates except for the trivial cases 1*F(j)=1*F(j) and F(i)*F(j)=F(j)*F(i). - Robert Israel, May 11 2016
The number 1 is included because 1 = F(1)*F(2). - Clark Kimberling, Jun 19 2016
LINKS
T. D. Noe, Table of n, a(n) for n=1..1000
Mohammad K. Azarian, The Value of a Series of Reciprocal Fibonacci Numbers, Problem B-1133, Fibonacci Quarterly, Vol. 51, No. 3, August 2013, p. 275. Solution published in Vol. 52, No. 3, August 2014, pp. 277-278.
MathOverflow, Distinctness of products of Fibonacci numbers
MAPLE
fib:= combinat:-fibonacci:
sort(convert(select(`<`, {0, seq(seq(fib(i)*fib(j), i=j+1..100), j=1..100)}, fib(101)), list)); # Robert Israel, May 11 2016
MATHEMATICA
Take[Union[Flatten[Table[Fibonacci[i]*Fibonacci[j], {i, 0, 100}, {j, i + 1, 100}]]], 100] (* Clark Kimberling, May 11 2016 *)
PROG
(PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
isok(n) = {if ((n==0) || (n==1), return (1)); fordiv(n, d, if (d^2 < n, if (isfib(d) && isfib(n/d), return (1)); ); ); return(0); } \\ Michel Marcus, May 27 2019
(PARI) lista(nn) = {my(out = List([0])); for (i=0, nn, for (j=i+1, nn, listput(out, fibonacci(i)*fibonacci(j)); ); ); Vec(vecsort(select(x->(x < fibonacci(nn+1)), out), , 8)); } \\ Michel Marcus, May 27 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name changed to conform with A272949 et al. by Clark Kimberling, Jun 18 2016
STATUS
approved