|
|
A001466
|
|
Denominators of greedy Egyptian fraction expansion of Pi - 3.
(Formerly M4553 N1935)
|
|
38
|
|
|
|
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
|
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.
|
|
EXAMPLE
|
Pi - 3 = 1/8 + 1/61 + 1/5020 + 1/128541455 + ... .
|
|
MATHEMATICA
|
|
|
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));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|