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 A130239 #17 Mar 18 2023 03:56:33
%S A130239 0,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,
%T A130239 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,
%U A130239 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6
%N A130239 Maximal index k of the square of a Fibonacci number such that Fib(k)^2 <= n (the 'lower' squared Fibonacci Inverse).
%H A130239 G. C. Greubel, <a href="/A130239/b130239.txt">Table of n, a(n) for n = 0..5000</a>
%F A130239 a(n) = max(k | Fib(k)^2 <= n) = A130233(floor(sqrt(n))).
%F A130239 a(n) = floor(arcsinh(sqrt(5n)/2)/log(phi)), where phi=(1+sqrt(5))/2.
%F A130239 G.f.: (1/(1-x))*Sum_{k>=1} x^(Fib(k)^2).
%e A130239 a(10) = 4 since Fib(4)^2 = 9 <= 10 but Fib(5)^2 = 25 > 10.
%t A130239 A130233[n_]:= Floor[Log[GoldenRatio, 3/2 +n*Sqrt[5]]];
%t A130239 Table[A130233[Floor[Sqrt[n]]], {n, 0, 120}] (* _G. C. Greubel_, Mar 18 2023 *)
%o A130239 (Magma)
%o A130239 A130233:= func< n | Floor(Log(3/2 + n*Sqrt(5))/Log((1+Sqrt(5))/2)) >;
%o A130239 [A130233(Floor(Sqrt(n))): n in [0..120]]; // _G. C. Greubel_, Mar 18 2023
%o A130239 (SageMath)
%o A130239 def A130233(n): return int(log(3/2 +n*sqrt(5), golden_ratio))
%o A130239 def A130239(n): return A130233(floor(sqrt(n)))
%o A130239 [A130239(n) for n in range(121)] # _G. C. Greubel_, Mar 18 2023
%Y A130239 Partial sums: A130240. Other related sequences: A000045, A130233, A130234, A130235, A130236, A130237, A130238, A130240, A130243, A130246, A130248, A130239, A130251, A130253, A130257, A130261.
%K A130239 nonn
%O A130239 0,2
%A A130239 _Hieronymus Fischer_, May 17 2007, May 28 2007