A006525 Denominators of greedy Egyptian fraction for e - 2.

2, 5, 55, 9999, 3620211523, 25838201785967533906, 3408847366605453091140558218322023440765

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• frac

Comments

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

Examples

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

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

Crossrefs

Cf. A006526, A269993.

Cf. A001466 (similar for Pi-3).

Programs

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 *)

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

Formula

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

Extensions

More terms from Herman P. Robinson

Offset changed to 1 by Indranil Ghosh, Mar 27 2017