

A270358


Denominators of rEgyptian fraction expansion for (1/2)^(1/3), where r = (1, 1/2, 1/4, 1/8, ...).


2



2, 2, 6, 62, 3526, 6487141, 39385964848219, 870200535339836766981506923, 7107112253865886739857942326428066600374758700504057908, 51149853017945104127158581151674618357470586573041429321297826264898103722100928190358789489996748918377200334
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OFFSET

1,1


COMMENTS

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(k1)), and f(k) = f(k1)  r(k)/n(k). Then x = r(1)/n(1) + r(2)/n(2) + r(3)/n(3) + ..., the rEgyptian fraction for x.
See A269993 for a guide to related sequences.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..12
Eric Weisstein's World of Mathematics, Egyptian Fraction
Index entries for sequences related to Egyptian fractions


EXAMPLE

(1/2)^(1/3) = 1/2 + 1/(2*2) + 1/(4*6) + ...


MATHEMATICA

r[k_] := 2/2^k; f[x_, 0] = x; z = 10;
n[x_, k_] := n[x, k] = Ceiling[r[k]/f[x, k  1]]
f[x_, k_] := f[x, k] = f[x, k  1]  r[k]/n[x, k]
x = (1/2)^(1/3); Table[n[x, k], {k, 1, z}]


CROSSREFS

Cf. A269993.
Sequence in context: A326942 A247943 A329571 * A156529 A184712 A303225
Adjacent sequences: A270355 A270356 A270357 * A270359 A270360 A270361


KEYWORD

nonn,frac,easy


AUTHOR

Clark Kimberling, Mar 20 2016


STATUS

approved



