A270555 Denominators of r-Egyptian fraction expansion for log(2), where r(k) = 1/(2k-1).

2, 2, 8, 97, 14319, 624706742, 650582824487459710, 603427782600234609340303332178054808, 537935638469864198057050787293558181575074487162482534612409868942679959

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..12

Eric Weisstein's World of Mathematics, Egyptian Fraction

Index entries for sequences related to Egyptian fractions

Example

log(2) = 1/(1*2) + 1/(3*2) + 1/(5*8) + 1/(7*97) + ...

Mathematica

r[k_] := 1/(2k-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 = Log[2]; Table[n[x, k], {k, 1, z}]

Crossrefs

Cf. A269993, A005408.

Sequence in context: A007848 A326906 A303060 * A270405 A047692 A270316

Adjacent sequences: A270552 A270553 A270554 * A270556 A270557 A270558

Keyword

nonn,frac,easy

Author

Clark Kimberling, Apr 03 2016

Status

approved