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 A270527 #10 Feb 16 2025 08:33:31
%S A270527 2,2,4,21,168,10754,25461498,105205312405537,
%T A270527 2273436544813042470905435068,
%U A270527 580632014636885174037652548241171956049642213022500047,105076738483143967759563061000636154401568577693011463452250666394865203888381724797435152416096091560375615
%N A270527 Denominators of r-Egyptian fraction expansion for (1/2)^(1/3), where r(k) = 1/k!.
%C A270527 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 A270527 See A269993 for a guide to related sequences.
%H A270527 Clark Kimberling, <a href="/A270527/b270527.txt">Table of n, a(n) for n = 1..13</a>
%H A270527 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H A270527 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e A270527 (1/2)^(1/3) = 1/(1*2) + 1/(2*2) + 1/(6*4) + 1/(24*21) + ...
%t A270527 r[k_] := 1/k!; f[x_, 0] = x; z = 10;
%t A270527 n[x_, k_] := n[x, k] = Ceiling[r[k]/f[x, k - 1]]
%t A270527 f[x_, k_] := f[x, k] = f[x, k - 1] - r[k]/n[x, k]
%t A270527 x = (1/2)^(1/3); Table[n[x, k], {k, 1, z}]
%Y A270527 Cf. A269993, A000142.
%K A270527 nonn,frac,easy
%O A270527 1,1
%A A270527 _Clark Kimberling_, Apr 02 2016