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

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

Adjacent sequences: A243366 A243367 A243368 * A243370 A243371 A243372

Keyword

nonn

Author

Arlu Genesis A. Padilla, Jun 04 2014

Status

approved