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%I M4553 N1935 #66 May 05 2020 02:03:32
%S 8,61,5020,128541455,162924332716605980,
%T 28783052231699298507846309644849796,
%U 871295615653899563300996782209332544845605756266650946342214549769447
%N Denominators of greedy Egyptian fraction expansion of Pi - 3.
%C A greedy Egyptian fraction expansion is also called a Sylvester expansion. - _Robert FERREOL_, May 02 2020
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Simon Plouffe, <a href="/A001466/b001466.txt">Table of n, a(n) for n = 1..10</a> (There is a limit of about 1000 digits on the size of numbers in b-files)
%H Mohammad K. Azarian, <a href="http://www.jstor.org/stable/27646572">An Expression for Pi, Problem #870</a>, College Mathematics Journal, Vol. 39, No. 1, January 2008, p. 66. <a href="http://www.jstor.org/stable/27646723">Solution</a> appeared in Vol. 40, No. 1, January 2009, pp. 62-64.
%H K. R. R. Gandhi, <a href="http://www.ijma.info/index.php/ijma/article/view/1587">Edifice of the real numbers by alternating series</a>, International Journal of Mathematical Archive-3(9), 2012, 3277-3280. - From _N. J. A. Sloane_, Jan 02 2013
%H Simon Plouffe, <a href="/A001466/a001466.txt">Table of n, a(n) for n = 1..14</a>
%H H. P. Robinson, <a href="/A001466/a001466.pdf">Letter to N. J. A. Sloane, Sep 1975</a>
%H H. E. Salzer, <a href="http://www.jstor.org/stable/2305906">The approximation of numbers as sums of reciprocals</a>, Amer. Math. Monthly, 54 (1947), 135-142.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Greedy_algorithm_for_Egyptian_fractions">Greedy algorithm for Egyptian fractions</a>
%H J. W. Wrench, Jr., <a href="/A001466/a001466.png">Letter to N. J. A. Sloane, Mar 27 1974</a>
%H <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>
%e Pi - 3 = 1/8 + 1/61 + 1/5020 + 1/128541455 + ... .
%t 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 *)
%o (PARI) x = Pi - 3;
%o f(x, k) = if(k<1, x, f(x, k - 1) - 1/n(x, k));
%o n(x, k) = ceil(1/f(x, k - 1));
%o for(k = 1, 7, print1(n(x, k), ", ")) \\ _Indranil Ghosh_, Mar 27 2017
%Y See A182257, A224230 for other versions of this sequence.
%Y Cf. A006525 (similar for e-2).
%K nonn,frac
%O 1,1
%A _N. J. A. Sloane_
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