

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

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 bfiles)
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. 6264.
K. R. R. Gandhi, Edifice of the real numbers by alternating series, International Journal of Mathematical Archive3(9), 2012, 32773280.  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), 135142.
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
Index entries for sequences related to the number Pi


EXAMPLE

Pi  3 = 1/8 + 1/61 + 1/5020 + 1/128541455 + ... .


MATHEMATICA

lst={}; k=N[(Pi3), 1000]; Do[s=Ceiling[1/k]; AppendTo[lst, s]; k=k1/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

See A182257, A224230 for other versions of this sequence.
Cf. A006525 (similar for e2).
Sequence in context: A254602 A327761 A080525 * A182257 A082179 A114028
Adjacent sequences: A001463 A001464 A001465 * A001467 A001468 A001469


KEYWORD

nonn,frac


AUTHOR

N. J. A. Sloane


STATUS

approved



