A388472 Decimal expansion of 2 * exp(-Pi/24) * Pi^(1/4) * Gamma(7/8) * (2-sqrt(2)) / Gamma(5/8).

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

Offset

1,3

Links

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

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

Index entries for transcendental numbers.

Formula

Empirical: Equals Sum_{k>=0} A085261(k) / exp(k*Pi).

Equals 2^(3/2) * sqrt(sqrt(2) - 1) * Pi^(3/4) / (exp(Pi/24) * Gamma(1/4)). - Vaclav Kotesovec, Jan 08 2026

Example

1.03941616230437494289667181102236179167881089268281354015912574887007720090....

Mathematica

First[RealDigits[(-2*(-2 + Sqrt[2])*Pi^(1/4)*Exp[-1/24*Pi]*Gamma[7/8])/Gamma[5/8], 10, 100]]
RealDigits[2^(3/2) * Sqrt[Sqrt[2] - 1] * Pi^(3/4) / (E^(Pi/24)*Gamma[1/4]), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) 2 * exp(-1/24 * Pi) * Pi^(1/4) * gamma(7/8) * (2-2^(1/2)) / gamma(5/8)
(PARI) 2^(3/2)*sqrt(sqrt(2)-1)*Pi^(3/4)/(exp(Pi/24)*gamma(1/4)) \\ Charles R Greathouse IV, Jul 18 2026

Crossrefs

Cf. A085261.

Sequence in context: A392968 A388642 A200012 * A130701 A202021 A342220

Adjacent sequences: A388469 A388470 A388471 * A388473 A388474 A388475

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 17 2025

Status

approved