A388679 Decimal expansion of exp(Pi/3)*(3 + sqrt(3))/18.

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

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Simon Plouffe, Numbers in the base e^Pi, 2025.

Index entries for transcendental numbers.

Formula

Empirical: Equals Sum_{k>=0} A164270(k) / exp(k*Pi).

Equals (1/24) * exp(Pi / 3) * Gamma(2/3)^2 * Gamma(7/12) * (1+3^(1/2))^2 / Gamma(11/12) / Pi.

Example

0.74915039320635340364432750743917203250...

Mathematica

First[RealDigits[Exp[Pi/3]*(3 + Sqrt[3])/18, 10, 100]] (* Paolo Xausa, Sep 19 2025 *)

Prog

(PARI) (1/24) * exp(Pi / 3) * gamma(2/3)^2 * gamma(7/12) * (1+3^(1/2))^2 / gamma(11/12) / Pi

Crossrefs

Cf. A164270.

Sequence in context: A381657 A119824 A383173 * A271173 A242909 A259147

Adjacent sequences: A388676 A388677 A388678 * A388680 A388681 A388682

Keyword

nonn,cons,easy

Author

Simon Plouffe, Sep 18 2025

Status

approved