A388670 Decimal expansion of 5 * (2+sqrt(5)) * exp(-Pi).

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

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

Index entries for transcendental numbers.

Formula

Empirical: Equals Sum_{k>=0} A145740(k) / exp(k*Pi).

Example

0.91528547669729468790179014129096541090226618725422320015347941941877369407....

Mathematica

First[RealDigits[5*(2 + Sqrt[5])*Exp[-Pi], 10, 100]]

Prog

(PARI) (128/625) * exp(-Pi) * 2^(1/5) * 5^(1/2) * gamma(9/10)^6 * gamma(7/10)^6 * (5+5^(1/2))^6 * (1/4*5^(1/2)-1/4)^6 * (1/4*5^(1/2)+1/4)^6 / gamma(4/5)^12

Crossrefs

Cf. A145740.

Sequence in context: A388779 A388705 A388617 * A388866 A388323 A100924

Adjacent sequences: A388667 A388668 A388669 * A388671 A388672 A388673

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved