A388522 Decimal expansion of (5^(1/4)+5^(3/4)) * exp(-Pi/2).

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

Offset

1,4

Links

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

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

Formula

Empirical: Equals Sum_{k>=0} A112180(k) / exp(k*Pi).

Equals exp(-Pi/2)*(5^(1/4) + 5^(3/4)). - Paolo Xausa, Sep 18 2025

Example

1.0059397275727851111129394294679447043...

Mathematica

First[RealDigits[Exp[-Pi/2]*(5^(1/4) + 5^(3/4)), 10, 100]] (* Paolo Xausa, Sep 18 2025 *)

Prog

(PARI) (8/25) * exp(-Pi / 2) * 2^(2/5) * 5^(3/4) * gamma(9/10)^2 * gamma(7/10)^2 * (5+5^(1/2))^2 * (1/4*5^(1/2)-1/4)^2 * (1/4*5^(1/2)+1/4)^2 / gamma(4/5)^4

Crossrefs

Cf. A112180.

Sequence in context: A111453 A222074 A388796 * A385193 A245735 A303497

Adjacent sequences: A388519 A388520 A388521 * A388523 A388524 A388525

Keyword

nonn,cons,easy

Author

Simon Plouffe, Sep 17 2025

Status

approved