A369881 Decimal expansion of 1/(2*sqrt(e)).

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

Table of n, a(n) for n=0..104.

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

Crossrefs

Cf. A001113, A019774, A019778, A066318, A092605, A187832, A249455.

Sequence in context: A112470 A331924 A201582 * A115379 A127801 A096597

Adjacent sequences: A369878 A369879 A369880 * A369882 A369883 A369884

Keyword

nonn,cons,easy

Author

Amiram Eldar, Feb 04 2024

Status

approved