

A269573


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


2




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.


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 + 1/4 + 1/23 + ...


MATHEMATICA

r[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 = 2^(1/3); Table[n[x, k], {k, 1, z}] (* A269573 *)


CROSSREFS

Cf. A269993 (guide to related sequences).
Sequence in context: A009317 A209024 A081680 * A147761 A214299 A090591
Adjacent sequences: A269570 A269571 A269572 * A269574 A269575 A269576


KEYWORD

nonn,frac,easy


AUTHOR

Clark Kimberling, Mar 15 2016


STATUS

approved



