The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A270483 Denominators of r-Egyptian fraction expansion for 1/E, where r(k) = 1/Prime(k). 1
2, 3, 30, 1406, 1566618, 3968926143121, 51168240940958042671940949, 13365052216163708497107274374215341296314835773754330, 1279540722856331753015023627177246106080657069367343330334092565051020739543151941507268082633550601641928 (list; graph; refs; listen; history; text; internal format)
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
Eric Weisstein's World of Mathematics, Egyptian Fraction
EXAMPLE
1/e = 1/(2*2) + 1/(3*3) + 1/(5*30) + 1/(7*1406) + ...
MATHEMATICA
r[k_] := 1/Prime[k]; 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/E; Table[n[x, k], {k, 1, z}]
CROSSREFS
Sequence in context: A137981 A110351 A326224 * A217370 A088115 A230627
KEYWORD
nonn,frac,easy
AUTHOR
Clark Kimberling, Mar 30 2016
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 30 15:08 EDT 2024. Contains 372968 sequences. (Running on oeis4.)