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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]

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

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Last modified May 16 09:28 EDT 2021. Contains 343940 sequences. (Running on oeis4.)