

A317855


Decimal expansion of a constant related to the asymptotics of A122400.


19



3, 1, 6, 1, 0, 8, 8, 6, 5, 3, 8, 6, 5, 4, 2, 8, 8, 1, 3, 8, 3, 0, 1, 7, 2, 2, 0, 2, 5, 8, 8, 1, 3, 2, 4, 9, 1, 7, 2, 6, 3, 8, 2, 7, 7, 4, 1, 8, 8, 5, 5, 6, 3, 4, 1, 6, 2, 7, 2, 7, 8, 2, 0, 7, 5, 3, 7, 6, 9, 7, 0, 5, 9, 2, 1, 9, 3, 0, 4, 6, 1, 1, 2, 1, 9, 7, 5, 7, 4, 6, 8, 5, 4, 9, 7, 8, 4, 5, 9, 3, 2, 4, 2, 2, 7
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OFFSET

1,1


LINKS



FORMULA

Equals (1+exp(1/r))*r^2, where r = 0.873702433239668330496568304720719298213992... is the root of the equation exp(1/r)/r + (1+exp(1/r))*LambertW(exp(1/r)/r) = 0.


EXAMPLE

3.161088653865428813830172202588132491726382774188556341627278...


MATHEMATICA

r = r /. FindRoot[E^(1/r)/r + (1 + E^(1/r)) * ProductLog[E^(1/r)/r] == 0, {r, 3/4}, WorkingPrecision > 120]; RealDigits[(1 + Exp[1/r])*r^2][[1]]


PROG

(PARI) r=solve(r=.8, 1, exp(1/r)/r + (1+exp(1/r))*lambertw(exp(1/r)/r))


CROSSREFS

Cf. A121886, A122399, A122400, A122418, A122419, A122420, A227619, A232192, A243802, A244585, A248798, A317340, A326010.


KEYWORD



AUTHOR



STATUS

approved



