OFFSET
1,1
COMMENTS
A greedy Egyptian fraction expansion is also called a Sylvester expansion. - Robert FERREOL, May 02 2020
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Simon Plouffe, Table of n, a(n) for n = 1..10 (There is a limit of about 1000 digits on the size of numbers in b-files)
Mohammad K. Azarian, An Expression for Pi, Problem #870, College Mathematics Journal, Vol. 39, No. 1, January 2008, p. 66. Solution appeared in Vol. 40, No. 1, January 2009, pp. 62-64.
K. R. R. Gandhi, Edifice of the real numbers by alternating series, International Journal of Mathematical Archive-3(9), 2012, 3277-3280. - From N. J. A. Sloane, Jan 02 2013
Simon Plouffe, Table of n, a(n) for n = 1..14
H. P. Robinson, Letter to N. J. A. Sloane, Sep 1975
H. E. Salzer, The approximation of numbers as sums of reciprocals, Amer. Math. Monthly, 54 (1947), 135-142.
Eric Weisstein's World of Mathematics, Egyptian Fraction
Wikipedia, Greedy algorithm for Egyptian fractions
J. W. Wrench, Jr., Letter to N. J. A. Sloane, Mar 27 1974
EXAMPLE
Pi - 3 = 1/8 + 1/61 + 1/5020 + 1/128541455 + ... .
MATHEMATICA
lst={}; k=N[(Pi-3), 1000]; 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 = Pi - 3;
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
STATUS
approved