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A270527 Denominators of r-Egyptian fraction expansion for (1/2)^(1/3), where r(k) = 1/k!. 2
2, 2, 4, 21, 168, 10754, 25461498, 105205312405537, 2273436544813042470905435068, 580632014636885174037652548241171956049642213022500047, 105076738483143967759563061000636154401568577693011463452250666394865203888381724797435152416096091560375615 (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..13

Eric Weisstein's World of Mathematics, Egyptian Fraction

Index entries for sequences related to Egyptian fractions

EXAMPLE

(1/2)^(1/3) = 1/(1*2) + 1/(2*2) + 1/(6*4) + 1/(24*21) + ...

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, A000142.

Sequence in context: A287745 A287909 A263439 * A232275 A257612 A009541

Adjacent sequences:  A270524 A270525 A270526 * A270528 A270529 A270530

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Apr 02 2016

STATUS

approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)