A388374 Decimal expansion of (1/256) * 3^(1/2) * Gamma(2/3) * Gamma(5/8)^8 * Gamma(11/12)^2 * Gamma(7/12)^3 * (17+12 * sqrt(2)) * (1+3^(1/2)) * sqrt(2) * (2+sqrt(2))^(1/2) / Pi^(15/4) / Gamma(7/8)^8.

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

Offset

1,3

Links

Table of n, a(n) for n=1..90.

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

Formula

Empirical: Equals Sum_{k>=0} A029594(k) / exp(k*Pi).

Equals sqrt((1 + sqrt(2))*(1 + sqrt(3))) * Gamma(1/4)^3 / (2^(5/2) * 3^(3/8) * Pi^(9/4)). - Vaclav Kotesovec, Jan 07 2026

Example

1.0906685252637721465886329510172164776...

Mathematica

RealDigits[(Sqrt[(1 + Sqrt[2])*(1 + Sqrt[3])] * Gamma[1/4]^3) / (2^(5/2) * 3^(3/8) * Pi^(9/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 07 2026 *)

Prog

(PARI) (1/256) * 3^(1/2) * gamma(2/3) * gamma(5/8)^8 * gamma(11/12)^2 * gamma(7/12)^3 * (17+12 * sqrt(2)) * (1+3^(1/2)) * sqrt(2) * (2+2^(1/2))^(1/2) / Pi^(15/4) / gamma(7/8)^8

Crossrefs

Cf. A029594.

Sequence in context: A225464 A296566 A198213 * A381497 A388756 A388555

Adjacent sequences: A388371 A388372 A388373 * A388375 A388376 A388377

Keyword

nonn,cons

Author

Simon Plouffe, Sep 15 2025

Extensions

Data corrected by Paolo Xausa, Jan 07 2026

Status

approved