A389055 - OEIS

A389055

Decimal expansion of (sqrt((3 * (4+2 * sqrt(5)+sqrt(3 * (9+4 * sqrt(5))))) / 5) * Pi^(1/4) * Gamma(7/12)^3 * Gamma(2/3) * Gamma(11/12)^2) / (4 * Gamma(3/4)^8).

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

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..87.

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

FORMULA

Empirical: Equals Sum_{k>=0} A320239(k) / exp(k*Pi).

Equals sqrt(1 + sqrt(3)) * (1 + sqrt(5))^(3/2) * Gamma(1/4)^3 / (2^(13/4) * 3^(3/8) * sqrt(5) * Pi^(9/4)). - Vaclav Kotesovec, Jan 09 2026

EXAMPLE

1.0866104882516378755410636489106252048...

MATHEMATICA

First[RealDigits[(Sqrt[(3*(4 + 2*Sqrt[5] + Sqrt[3*(9 + 4*Sqrt[5])]))/5]*Pi^(1/4)*Gamma[7/12]^3*Gamma[2/3]*Gamma[11/12]^2)/(4*Gamma[3/4]^8), 10, 100]]

RealDigits[Sqrt[1 + Sqrt[3]]*(1 + Sqrt[5])^(3/2)*Gamma[1/4]^3 / (2^(13/4)*3^(3/8)*Sqrt[5]*Pi^(9/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

PROG

(PARI) -(1/6400) * 3^(1/2) * 5^(3/4) * Pi^(1/4) * gamma(2/3) * gamma(7/12)^3 * gamma(11/12)^2 * (1+3^(1/2))^3 * (-2+3^(1/2)) * (5-5^(1/2))^(3/2) * (5^(1/2)+1)^3 / gamma(3/4)^8

CROSSREFS

Cf. A320239.

Sequence in context: A010527 A270137 A388392 * A269846 A316136 A102887

Adjacent sequences: A389052 A389053 A389054 * A389056 A389057 A389058

KEYWORD

nonn,cons

AUTHOR

Simon Plouffe, Sep 22 2025

STATUS

approved