A382907 Decimal expansion of 1/2 - Pi*(sqrt(2)+1)/16.

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

Offset

0,2

Links

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

I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products (6th ed.), 2000, (eq. 0.239.7).

Index entries for transcendental numbers.

Formula

Equals Sum_{k>=1} 1/((8*k-1)*(8*k+1)).

From Amiram Eldar, Aug 08 2025: (Start)

Equals Sum_{k>=1} 1/A158684(k).

Equals (1 - cot(Pi/8)*Pi/8)/2. (End)

Example

0.02597027551574003215759...

Mathematica

Join[{0}, RealDigits[1/2-(Pi(Sqrt[2]+1))/16, 10, 120][[1]]] (* Harvey P. Dale, Apr 30 2025 *)

Prog

(PARI) 1/2-Pi*(sqrt(2)+1)/16 \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Cf. A158684, A239120.

Sequence in context: A204913 A198455 A339174 * A018878 A021389 A198429

Adjacent sequences: A382904 A382905 A382906 * A382908 A382909 A382910

Keyword

nonn,cons

Author

Sean A. Irvine, Apr 08 2025

Status

approved