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A219114 Integers n such that n^2 is the difference of two Fibonacci numbers. 5
0, 1, 2, 4, 9, 12, 15, 24 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 20 11:01 EST 2020. Contains 331083 sequences. (Running on oeis4.)