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A243369
Denominators of Egyptian fraction expansion of e, without repetition.
1
1, 2, 3, 4, 5, 6, 7, 8, 2355, 17497263, 1860801514823609, 3584505381349378370871887741627, 85751894581999497691951513557530024967086681471033652102477414
OFFSET
1,2
COMMENTS
Slightly different version of A073422, disregarding the repetition of values.
Similar process to A243020 (Denominators of Egyptian fraction expansion of Pi, without repetition).
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
LINKS
Arlu Genesis A. Padilla, Table of n, a(n) for n = 1..17
EXAMPLE
e = 1 + 1/2 + 1/3 + ... + 1/8 + 1/2355 + ...
MAPLE
Digits := 1000:
a243369set := {1} ;
for loop from 1 to 13 do
erest := evalf(exp(1))-add(1/p, p=a243369set) ;
eivn := ceil(1/erest) ;
while eivn in a243369set do
eivn := eivn+1 ;
end do:
a243369set := a243369set union {eivn} ;
print(eivn) ;
end do: # R. J. Mathar, Jul 03 2017
CROSSREFS
Cf. A073422.
Sequence in context: A365822 A004903 A004914 * A228052 A308072 A084689
KEYWORD
nonn
AUTHOR
STATUS
approved