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A006525 Denominators of greedy Egyptian fraction for e - 2.

%I A006525 M1553 #56 Feb 16 2025 08:32:30
%S A006525 2,5,55,9999,3620211523,25838201785967533906,
%T A006525 3408847366605453091140558218322023440765
%N A006525 Denominators of greedy Egyptian fraction for e - 2.
%C A006525 A greedy Egyptian fraction is also called a Sylvester expansion. - _Robert FERREOL_, May 02 2020
%D A006525 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006525 Vincenzo Librandi, <a href="/A006525/b006525.txt">Table of n, a(n) for n = 1..11</a> [a(11) corrected by _Georg Fischer_, Jun 22 2020]
%H A006525 H. P. Robinson, <a href="/A001466/a001466.pdf">Letter to N. J. A. Sloane, Sep 1975</a>
%H A006525 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H A006525 Wikipedia, <a href="https://en.wikipedia.org/wiki/Greedy_algorithm_for_Egyptian_fractions">Greedy algorithm for Egyptian fractions</a>
%H A006525 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%F A006525 a(n) = ceiling(1/(e - 2 - Sum_{j=0..n-1} 1/a(j))). - _Jon E. Schoenfield_, Dec 26 2014
%e A006525 e - 2 = 1/2 + 1/5 + 1/55 + 1/9999 + ... . - _Jon E. Schoenfield_, Dec 26 2014
%t A006525 lst={};k=N[E-2,1000000];Do[s=Ceiling[1/k];AppendTo[lst,s];k=k-1/s,{n,12}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 02 2009 *)
%o A006525 (PARI) x = exp(1) - 2;
%o A006525 f(x, k) = if(k<1, x, f(x, k - 1) - 1/n(x, k));
%o A006525 n(x, k) = ceil(1/f(x, k - 1));
%o A006525 for(k = 1, 7, print1(n(x, k), ", ")) \\ _Indranil Ghosh_, Mar 27 2017
%Y A006525 Cf. A006526, A269993.
%Y A006525 Cf. A001466 (similar for Pi-3).
%K A006525 nonn,frac
%O A006525 1,1
%A A006525 _N. J. A. Sloane_
%E A006525 More terms from _Herman P. Robinson_
%E A006525 Offset changed to 1 by _Indranil Ghosh_, Mar 27 2017