

A219114


Integers n such that n^2 is the difference of two Fibonacci numbers.


5




OFFSET

1,3


COMMENTS

Numbers n such that n^2 is in A007298.
No other terms below 10^10000.  Manfred Scheucher, Jun 12 2015


LINKS

Table of n, a(n) for n=1..8.
MathOverflow, Can the difference of two distinct Fibonacci numbers be a square infinitely often?
Manfred Scheucher, Sage Script


EXAMPLE

The only known square differences of Fibonacci numbers are:
0^2 = F(2)F(1) = F(k)F(k) for any k,
1^2 = F(1)F(0) = F(2)F(0) = F(3)F(1) = F(3)F(2) = F(4)F(3),
2^2 = F(5)F(1) = F(5)F(2),
4^2 = F(8)F(5),
9^2 = F(11)F(6),
12^2 = F(12)F(0) = F(13)F(11) = F(14)F(13),
15^2 = F(13)F(6),
24^2 = F(15)F(9).


MATHEMATICA

t = Union[Flatten[Table[Fibonacci[n]  Fibonacci[i], {n, 100}, {i, n}]]]; t2 = Select[t, IntegerQ[Sqrt[#]] &]; Sqrt[t2] (* T. D. Noe, Feb 12 2013 *)


CROSSREFS

Cf. A000045 (Fibonacci numbers).
Cf. A007298 (differences of Fibonacci numbers).
Sequence in context: A096186 A175041 A298823 * A182859 A088901 A283147
Adjacent sequences: A219111 A219112 A219113 * A219115 A219116 A219117


KEYWORD

nonn,hard,more


AUTHOR

Max Alekseyev, Nov 12 2012


STATUS

approved



