A388676 - OEIS

A388676

Decimal expansion of (9 * sqrt((5+sqrt(5)) * Pi) * exp(Pi / 4)) / (32*5^(3/4) * Gamma(7/4)^2).

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

Index entries for transcendental numbers.

FORMULA

Empirical: Equals Sum_{k>=0} A159818(k) / exp(k*Pi).

EXAMPLE

1.04134648148157625968498522056697048032070070350137463485054097630697857994....

MATHEMATICA

First[RealDigits[(9*Sqrt[(5 + Sqrt[5])*Pi]*Exp[Pi/4])/(32*5^(3/4)*Gamma[7/4]^2), 10, 100]]

PROG

(PARI) (1/1250) * exp(Pi / 4) * sqrt(Pi) * 2^(9/10) * gamma(9/10)^2 * gamma(7/10)^2 * (1/4*5^(1/2)-1/4)^2 * (1/4*5^(1/2)+1/4)^2*5^(1/2) * (5^(1/2) * sqrt(2) * (5+5^(1/2))^(1/2))^(7/2) * 2 / (2^(1/2) * (5+5^(1/2))^(1/2))^(1/2) / gamma(3/4)^2 / gamma(4/5)^4

CROSSREFS

Cf. A159818.

Sequence in context: A362331 A376264 A388569 * A058303 A240935 A388377

Adjacent sequences: A388673 A388674 A388675 * A388677 A388678 A388679

KEYWORD

nonn,cons

AUTHOR

Simon Plouffe, Sep 18 2025

STATUS

approved