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A243369
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Denominators of Egyptian fraction expansion of e, without repetition.
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1
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1, 2, 3, 4, 5, 6, 7, 8, 2355, 17497263, 1860801514823609, 3584505381349378370871887741627, 85751894581999497691951513557530024967086681471033652102477414
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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e = 1 + 1/2 + 1/3 + ... + 1/8 + 1/2355 + ...
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MAPLE
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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) ;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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