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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]
Eric Weisstein's World of Mathematics, Egyptian Fraction
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. A001466 (similar for Pi-3).
Sequence in context: A114029 A013171 A073422 * A254406 A260654 A339167
KEYWORD
nonn,frac
AUTHOR
EXTENSIONS
More terms from Herman P. Robinson
Offset changed to 1 by Indranil Ghosh, Mar 27 2017
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)