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
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
KEYWORD
nonn,frac
AUTHOR
EXTENSIONS
More terms from Herman P. Robinson
Offset changed to 1 by Indranil Ghosh, Mar 27 2017
STATUS
approved