This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A219114 #18 Feb 16 2025 04:08:33
%S A219114 0,1,2,4,9,12,15,24
%N A219114 Integers n such that n^2 is the difference of two Fibonacci numbers.
%C A219114 Numbers n such that n^2 is in A007298.
%C A219114 No other terms below 10^10000. - _Manfred Scheucher_, Jun 12 2015
%H A219114 MathOverflow, <a href="http://mathoverflow.net/questions/84797">Can the difference of two distinct Fibonacci numbers be a square infinitely often?</a>
%H A219114 Manfred Scheucher, <a href="/A219114/a219114.sage.txt">Sage Script</a>
%e A219114 The only known square differences of Fibonacci numbers are:
%e A219114 0^2 = F(2)-F(1) = F(k)-F(k) for any k,
%e A219114 1^2 = F(1)-F(0) = F(2)-F(0) = F(3)-F(1) = F(3)-F(2) = F(4)-F(3),
%e A219114 2^2 = F(5)-F(1) = F(5)-F(2),
%e A219114 4^2 = F(8)-F(5),
%e A219114 9^2 = F(11)-F(6),
%e A219114 12^2 = F(12)-F(0) = F(13)-F(11) = F(14)-F(13),
%e A219114 15^2 = F(13)-F(6),
%e A219114 24^2 = F(15)-F(9).
%t A219114 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 *)
%Y A219114 Cf. A000045 (Fibonacci numbers).
%Y A219114 Cf. A007298 (differences of Fibonacci numbers).
%K A219114 nonn,hard,more
%O A219114 1,3
%A A219114 _Max Alekseyev_, Nov 12 2012