login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006525 Denominators of greedy Egyptian fraction for e - 2.
(Formerly M1553)
29
2, 5, 55, 9999, 3620211523, 25838201785967533906, 3408847366605453091140558218322023440765 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A greedy Egyptian fraction is also called a Sylvester expansion. - Robert FERREOL, May 02 2020

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..11 [a(11) corrected by Georg Fischer, Jun 22 2020]

H. P. Robinson, Letter to N. J. A. Sloane, Sep 1975

Eric Weisstein's World of Mathematics, Egyptian Fraction

Wikipedia, Greedy algorithm for Egyptian fractions

Index entries for sequences related to Egyptian fractions

FORMULA

a(n) = ceiling(1/(e - 2 - Sum_{j=0..n-1} 1/a(j))). - Jon E. Schoenfield, Dec 26 2014

EXAMPLE

e - 2 = 1/2 + 1/5 + 1/55 + 1/9999 + ... . - Jon E. Schoenfield, Dec 26 2014

MATHEMATICA

lst={}; k=N[E-2, 1000000]; Do[s=Ceiling[1/k]; AppendTo[lst, s]; k=k-1/s, {n, 12}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 02 2009 *)

PROG

(PARI) x = exp(1) - 2;

f(x, k) = if(k<1, x, f(x, k - 1) - 1/n(x, k));

n(x, k) = ceil(1/f(x, k - 1));

for(k = 1, 7, print1(n(x, k), ", ")) \\ Indranil Ghosh, Mar 27 2017

CROSSREFS

Cf. A006526, A269993.

Cf. A001466 (similar for Pi-3).

Sequence in context: A114029 A013171 A073422 * A254406 A260654 A339167

Adjacent sequences: A006522 A006523 A006524 * A006526 A006527 A006528

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Herman P. Robinson

Offset changed to 1 by Indranil Ghosh, Mar 27 2017

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 December 8 10:24 EST 2022. Contains 358693 sequences. (Running on oeis4.)