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A243369 Denominators of Egyptian fraction expansion of e, without repetition.

%I A243369 #21 Aug 02 2018 08:54:15
%S A243369 1,2,3,4,5,6,7,8,2355,17497263,1860801514823609,
%T A243369 3584505381349378370871887741627,
%U A243369 85751894581999497691951513557530024967086681471033652102477414
%N A243369 Denominators of Egyptian fraction expansion of e, without repetition.
%C A243369 Slightly different version of A073422, disregarding the repetition of values.
%C A243369 Similar process to A243020 (Denominators of Egyptian fraction expansion of Pi, without repetition).
%C A243369 The integer terms a(1), a(2), ... approximate Euler's constant A001113 = 1/a(1) + 1/a(2) + 1/a(3)+... by a(1)=1 and then selecting a(n) as the smallest positive number not yet in {a(1),...,a(n-1)} such that the remainder A001113 -1/a(1) -1/a(2) ... -1/a(n) remains positive. - _R. J. Mathar_, Jul 03 2017
%H A243369 Arlu Genesis A. Padilla, <a href="/A243369/b243369.txt">Table of n, a(n) for n = 1..17</a>
%e A243369 e = 1 + 1/2 + 1/3 + ... + 1/8 + 1/2355 + ...
%p A243369 Digits := 1000:
%p A243369 a243369set := {1} ;
%p A243369 for loop from 1 to 13 do
%p A243369     erest := evalf(exp(1))-add(1/p,p=a243369set) ;
%p A243369     eivn := ceil(1/erest) ;
%p A243369     while eivn in a243369set do
%p A243369         eivn := eivn+1 ;
%p A243369     end do:
%p A243369     a243369set := a243369set union {eivn} ;
%p A243369     print(eivn) ;
%p A243369 end do: # _R. J. Mathar_, Jul 03 2017
%Y A243369 Cf. A073422.
%K A243369 nonn
%O A243369 1,2
%A A243369 _Arlu Genesis A. Padilla_, Jun 04 2014