

A270557


Denominators of rEgyptian fraction expansion for (1/2)^(1/3), where r(k) = 1/(2k1).


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.
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/(3*2) + 1/(5*2) + 1/(7*6) + ...


MATHEMATICA

r[k_] := 1/(2k1); 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, A005408.
Sequence in context: A321741 A101416 A098920 * A129365 A125838 A021453
Adjacent sequences: A270554 A270555 A270556 * A270558 A270559 A270560


KEYWORD

nonn,frac,easy


AUTHOR

Clark Kimberling, Apr 03 2016


STATUS

approved



