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A369881
Decimal expansion of 1/(2*sqrt(e)).
0
3, 0, 3, 2, 6, 5, 3, 2, 9, 8, 5, 6, 3, 1, 6, 7, 1, 1, 8, 0, 1, 8, 9, 9, 7, 6, 7, 4, 9, 5, 5, 9, 0, 2, 2, 6, 7, 2, 0, 9, 5, 9, 0, 6, 7, 7, 4, 3, 5, 9, 3, 4, 7, 7, 8, 4, 1, 4, 4, 6, 0, 7, 9, 3, 6, 7, 5, 2, 8, 2, 5, 9, 7, 0, 6, 8, 7, 4, 2, 1, 1, 9, 9, 9, 3, 2, 3, 8, 0, 5, 7, 5, 3, 9, 9, 4, 7, 2, 8, 0, 1, 3, 2, 1, 1
OFFSET
0,1
LINKS
D. M. Batinetu-Giurgiu, Problem 764, The Pentagon, Vol. 75, No. 2 (2016), p. 22.
Toyesh Prakash Sharma, The Applications of the Stirling's approximation to find limits, Revista Electronica MateInfo.ro, December 2020, pp. 44-49. See Problem 13, p. 49.
FORMULA
Equals A092605 / 2.
Equals exp(-(1 + A187832)).
Equals Sum_{n>=1} (-1)^(n+1)/A066318(n).
Equals lim_{n->oo} sqrt(n)*(((n+1)!)^(1/(2*(n+1))) - (n!)^(1/(2*n))) (Batinetu-Giurgiu, 2016).
EXAMPLE
0.30326532985631671180189976749559022672095906774359...
MATHEMATICA
RealDigits[1/(2*Sqrt[E]), 10, 105][[1]]
PROG
(PARI) exp(-1/2)/2
KEYWORD
nonn,cons,easy
AUTHOR
Amiram Eldar, Feb 04 2024
STATUS
approved