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A270358 Denominators of r-Egyptian 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 (list; graph; refs; listen; history; text; internal format)
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(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.

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

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Last modified December 2 09:52 EST 2020. Contains 338876 sequences. (Running on oeis4.)