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 A270405 #12 Feb 16 2025 08:33:31
%S A270405 2,2,8,99,9153,134325943,17980902816814494,
%T A270405 336913028495678415812394391065577,
%U A270405 70730509948452535771375914216285436007372776802180962851035180747
%N A270405 Denominators of r-Egyptian fraction expansion for (1/2)^(1/3), where r(k) = 1/Fibonacci(k+1).
%C A270405 Suppose that r is a sequence of rational numbers r(k) <= 1 for k >= 1, and that x is an irrational number in (0,1). Let f(0) = x, n(k) = floor(r(k)/f(k-1)), and f(k) = f(k-1) - r(k)/n(k). Then x = r(1)/n(1) + r(2)/n(2) + r(3)/n(3) + ..., the r-Egyptian fraction for x.
%C A270405 See A269993 for a guide to related sequences.
%H A270405 Clark Kimberling, <a href="/A270405/b270405.txt">Table of n, a(n) for n = 1..12</a>
%H A270405 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H A270405 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e A270405 (1/2)^(1/3) = 1/2 + 1/(2*2) + 1/(3*8) + 1/(5*99) + ...
%t A270405 r[k_] := 1/Fibonacci[k+1]; f[x_, 0] = x; z = 10;
%t A270405 n[x_, k_] := n[x, k] = Ceiling[r[k]/f[x, k - 1]]
%t A270405 f[x_, k_] := f[x, k] = f[x, k - 1] - r[k]/n[x, k]
%t A270405 x = (1/2)^(1/3); Table[n[x, k], {k, 1, z}]
%Y A270405 Cf. A269993, A000045, A270714.
%K A270405 nonn,frac,easy
%O A270405 1,1
%A A270405 _Clark Kimberling_, Mar 30 2016