A388685 - OEIS

A388685

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

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

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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} A169784(k) / exp(k*Pi).

EXAMPLE

1.18034095477483093834816034538442166469195109896638125162841452249691191032....

MATHEMATICA

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

PROG

(PARI) (8/125) * Pi^(3/4) * 2^(3/5) * 5^(1/4) * gamma(9/10)^3 * gamma(7/10)^3 * (5+5^(1/2))^3 * (1/4*5^(1/2)-1/4)^3 * (1/4*5^(1/2)+1/4)^3 / gamma(3/4)^3 / gamma(4/5)^6

CROSSREFS

Cf. A169784.

Sequence in context: A020837 A248679 A175574 * A388824 A388861 A388639

Adjacent sequences: A388682 A388683 A388684 * A388686 A388687 A388688

KEYWORD

nonn,cons

AUTHOR

Simon Plouffe, Sep 18 2025

STATUS

approved