

A006525


Denominators of greedy Egyptian fraction for e  2.
(Formerly M1553)


29




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..n1} 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[E2, 1000000]; Do[s=Ceiling[1/k]; AppendTo[lst, s]; k=k1/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 Pi3).
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



