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 A270316 #11 Feb 16 2025 08:33:31
%S A270316 2,2,8,123,149367,19877572990,3398650153657920854371,
%T A270316 38501744904404393452660892011327652171148221,
%U A270316 1751742507912624184333715455628345093210972368514121272905550101268413741408122585972087
%N A270316 Denominators of r-Egyptian fraction expansion for (1/2)^(1/3), where r = (1,1/2,1/3,1/4,...)
%C A270316 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 A270316 See A269993 for a guide to related sequences.
%H A270316 Clark Kimberling, <a href="/A270316/b270316.txt">Table of n, a(n) for n = 1..11</a>
%H A270316 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H A270316 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e A270316 (1/2)^(1/3) = 1/2 + 1/(2*2) + 1/(3*8) + ...
%t A270316 r[k_] := 1/k; f[x_, 0] = x; z = 10;
%t A270316 n[x_, k_] := n[x, k] = Ceiling[r[k]/f[x, k - 1]]
%t A270316 f[x_, k_] := f[x, k] = f[x, k - 1] - r[k]/n[x, k]
%t A270316 x = (1/2)^(1/3); Table[n[x, k], {k, 1, z}]
%Y A270316 Cf. A269993.
%K A270316 nonn,frac,easy
%O A270316 1,1
%A A270316 _Clark Kimberling_, Mar 17 2016