A388488 - OEIS

A388488

Decimal expansion of (3^(1/12) * exp(-Pi/24) * (((1+sqrt(3)) * Gamma(2/3) * Gamma(3/4)) / Gamma(11/12))^(2/3)) / (2^(19/24) * Pi^(1/3)).

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

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OFFSET

1,5

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} A097242(k) / exp(k*Pi).

Equals (1 + sqrt(3))^(1/3) / (2^(7/24) * exp(Pi/24)). - Vaclav Kotesovec, Jan 08 2026

EXAMPLE

1.0019517936255842155118110615632460217...

MATHEMATICA

First[RealDigits[(3^(1/12)*Exp[-1/24*Pi]*(((1 + Sqrt[3])*Gamma[2/3]*Gamma[3/4])/Gamma[11/12])^(2/3))/(2^(19/24)*Pi^(1/3)), 10, 100]]

RealDigits[(1 + Sqrt[3])^(1/3) / (2^(7/24)*E^(Pi/24)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

PROG

(PARI) (1/4) * exp(-1/24 * Pi) * 2^(7/8) * 3^(1/12) * gamma(2/3)^(2/3) * gamma(3/4)^(2/3) * (2^(1/2) * (1+3^(1/2)))^(2/3) / gamma(11/12)^(2/3) / Pi^(1/3)

CROSSREFS

Cf. A097242.

Sequence in context: A262178 A388767 A388882 * A154483 A198560 A391310

Adjacent sequences: A388485 A388486 A388487 * A388489 A388490 A388491

KEYWORD

nonn,cons

AUTHOR

Simon Plouffe, Sep 17 2025

STATUS

approved