

A270591


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


2




OFFSET

1,2


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) + 1/(3*2) + 1/(4*2) + 1/(5*99) + ...


MATHEMATICA

r[k_] := 1/(k+1); 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: A166996 A133295 A055470 * A210467 A156524 A194027
Adjacent sequences: A270588 A270589 A270590 * A270592 A270593 A270594


KEYWORD

nonn,frac,easy


AUTHOR

Clark Kimberling, Apr 04 2016


STATUS

approved



