A346441 Decimal expansion of the constant Sum_{k>=0} (-1)^k/(3*k)!.

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

Offset: 0

Author

Sean A. Irvine, Jul 17 2021

Keywords

• nonn
• cons

Examples

			0.8347194685772109622192832392...
		

Links

• Peter Bala, A continued fraction for A346441
• D. Bowman and J. Mc Laughlin, Polynomial continued fractions, Acta Arith. 103 (2002), no. 4, 329-342.
• Michael I. Shamos, A catalog of the real numbers (2011).

Crossrefs

Cf. A068985, A049470, A143819, A346440, A346439, A346438, A346437, A346436, A346435, A196498.

Programs

Mathematica

RealDigits[Sum[(-1)^k/(3*k)!, {k, 0, Infinity}], 10, 100][[1]] (* Amiram Eldar, Jul 18 2021 *)

PARI

sumalt(k=0, (-1)^k/(3*k)!) \\ Michel Marcus, Jul 18 2021

Formula

Equals 1/(3*e) + 2*sqrt(e)*cos(sqrt(3)/2)/3. - Amiram Eldar, Jul 18 2021

Continued fraction: 1/(1 + 1/(5 + 6/(119 + 120/(503 + ... + P(n-1)/((P(n) - 1) + ... ))))), where P(n) = (3*n)*(3*n - 1)*(3*n - 2) for n >= 1. See Bowman and Mc Laughlin, Corollary 10, p. 341 with m = 1, who also show that the constant is irrational. - Peter Bala, Feb 21 2024