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A270316 Denominators of r-Egyptian fraction expansion for (1/2)^(1/3), where r = (1,1/2,1/3,1/4,...) 2
2, 2, 8, 123, 149367, 19877572990, 3398650153657920854371, 38501744904404393452660892011327652171148221, 1751742507912624184333715455628345093210972368514121272905550101268413741408122585972087 (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..11

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/(3*8) + ...

MATHEMATICA

r[k_] := 1/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: A270555 A270405 A047692 * A069561 A180370 A326939

Adjacent sequences:  A270313 A270314 A270315 * A270317 A270318 A270319

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Mar 17 2016

STATUS

approved

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Last modified January 21 10:26 EST 2020. Contains 331105 sequences. (Running on oeis4.)