

A270405


Denominators of rEgyptian fraction expansion for (1/2)^(1/3), where r(k) = 1/Fibonacci(k+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.
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/(2*2) + 1/(3*8) + 1/(5*99) + ...


MATHEMATICA

r[k_] := 1/Fibonacci[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, A000045, A270714.
Sequence in context: A326906 A303060 A270555 * A047692 A270316 A069561
Adjacent sequences: A270402 A270403 A270404 * A270406 A270407 A270408


KEYWORD

nonn,frac,easy


AUTHOR

Clark Kimberling, Mar 30 2016


STATUS

approved



