cp's OEIS Frontend

A001466 Denominators of greedy Egyptian fraction expansion of Pi - 3.

%I A001466 M4553 N1935 #67 Feb 16 2025 08:32:23
%S A001466 8,61,5020,128541455,162924332716605980,
%T A001466 28783052231699298507846309644849796,
%U A001466 871295615653899563300996782209332544845605756266650946342214549769447
%N A001466 Denominators of greedy Egyptian fraction expansion of Pi - 3.
%C A001466 A greedy Egyptian fraction expansion is also called a Sylvester expansion. - _Robert FERREOL_, May 02 2020
%D A001466 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001466 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001466 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 A001466 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 A001466 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 A001466 Simon Plouffe, <a href="/A001466/a001466.txt">Table of n, a(n) for n = 1..14</a>
%H A001466 H. P. Robinson, <a href="/A001466/a001466.pdf">Letter to N. J. A. Sloane, Sep 1975</a>
%H A001466 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 A001466 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H A001466 Wikipedia, <a href="https://en.wikipedia.org/wiki/Greedy_algorithm_for_Egyptian_fractions">Greedy algorithm for Egyptian fractions</a>
%H A001466 J. W. Wrench, Jr., <a href="/A001466/a001466.png">Letter to N. J. A. Sloane, Mar 27 1974</a>
%H A001466 <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>
%e A001466 Pi - 3 = 1/8 + 1/61 + 1/5020 + 1/128541455 + ... .
%t A001466 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 A001466 (PARI) x = Pi - 3;
%o A001466 f(x, k) = if(k<1, x, f(x, k - 1) - 1/n(x, k));
%o A001466 n(x, k) = ceil(1/f(x, k - 1));
%o A001466 for(k = 1, 7, print1(n(x, k), ", ")) \\ _Indranil Ghosh_, Mar 27 2017
%Y A001466 See A182257, A224230 for other versions of this sequence.
%Y A001466 Cf. A006525 (similar for e-2).
%K A001466 nonn,frac
%O A001466 1,1
%A A001466 _N. J. A. Sloane_