A365066 Decimal expansion of the constant 1/0! - 1/1! + 1/2! + 1/3! - 1/4! + 1/5! + 1/6! - 1/7! + ...

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

Offset

0,1

Links

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

Formula

Equals e - 2*A143820.

Equals Sum_{n>=0} (-1)^(2^((n-1) mod 3) mod 2) / n! = e/3 - 4*sin(sqrt(3)/2 - Pi/6) / (3*sqrt(e)).

Equals Sum_{n>=0) 1/(3*n)! - 1/(3*n+1)! + 1/(3*n+2)!. - Michal Paulovic, Aug 19 2023

Example

0.63455111826122554275761424130960772236307995025163265587548911687697314...

Maple

Digits:=105: evalf(sum(1/(3*n)!-1/(3*n+1)!+1/(3*n+2)!, n=0..infinity)); # Michal Paulovic, Aug 20 2023

Mathematica

RealDigits[E/3 - (4*Sin[Sqrt[3]/2-Pi/6])/(3*Sqrt[E]), 10, 105][[1]]

Prog

(PARI) suminf(n=0, 1/(3*n)!-1/(3*n+1)!+1/(3*n+2)!) \\ Michal Paulovic, Aug 20 2023

Crossrefs

Cf. A143820.

Sequence in context: A350131 A167052 A222230 * A198110 A290795 A197577

Adjacent sequences: A365063 A365064 A365065 * A365067 A365068 A365069

Keyword

nonn,cons

Author

Peter McNair, Aug 19 2023

Status

approved