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%I #13 Feb 24 2018 10:10:23
%S 2,2,6,62,3526,6487141,39385964848219,870200535339836766981506923,
%T 7107112253865886739857942326428066600374758700504057908,
%U 51149853017945104127158581151674618357470586573041429321297826264898103722100928190358789489996748918377200334
%N Denominators of r-Egyptian fraction expansion for (1/2)^(1/3), where r = (1, 1/2, 1/4, 1/8, ...).
%C 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 See A269993 for a guide to related sequences.
%H Clark Kimberling, <a href="/A270358/b270358.txt">Table of n, a(n) for n = 1..12</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e (1/2)^(1/3) = 1/2 + 1/(2*2) + 1/(4*6) + ...
%t r[k_] := 2/2^k; f[x_, 0] = x; z = 10;
%t n[x_, k_] := n[x, k] = Ceiling[r[k]/f[x, k - 1]]
%t f[x_, k_] := f[x, k] = f[x, k - 1] - r[k]/n[x, k]
%t x = (1/2)^(1/3); Table[n[x, k], {k, 1, z}]
%Y Cf. A269993.
%K nonn,frac,easy
%O 1,1
%A _Clark Kimberling_, Mar 20 2016
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