A388517 Decimal expansion of exp(-Pi)*2*(5 + 3*sqrt(5)).

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

Offset

1,5

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

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

Index entries for transcendental numbers.

Formula

Equals (64/125) * exp(-Pi) * 2^(4/5) * 5^(1/2) * Gamma(9/10)^4 * Gamma(7/10)^4 * (5+5^(1/2))^4 * (1/4*5^(1/2)-1/4)^4 * (1/4*5^(1/2)+1/4)^4 / Gamma(4/5)^8.

Empirical: Equals Sum_{k>=0} A112158(k) / exp(k*Pi).

Example

1.0119147355092091259333126952057024705...

Mathematica

First[RealDigits[Exp[-Pi]*2*(5 + 3*Sqrt[5]), 10, 100]] (* Paolo Xausa, Sep 18 2025 *)

Prog

(PARI) (64/125) * exp(-Pi) * 2^(4/5) * 5^(1/2) * gamma(9/10)^4 * gamma(7/10)^4 * (5+5^(1/2))^4 * (1/4*5^(1/2)-1/4)^4 * (1/4*5^(1/2)+1/4)^4 / gamma(4/5)^8

Crossrefs

Cf. A112158.

Sequence in context: A089564 A178745 A114893 * A089101 A388467 A359809

Adjacent sequences: A388514 A388515 A388516 * A388518 A388519 A388520

Keyword

nonn,cons,easy

Author

Simon Plouffe, Sep 17 2025

Status

approved