A232272 Decimal expansion of arctan(1/Pi).

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

Offset

0,1

References

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 35, page 338.

Links

Table of n, a(n) for n=0..84.

Formula

Equals A019669 - A232273.

Equals Sum_{i>=0} (-1)^k/((1+2*k)*Pi^(1+2*k)).

From Wolfe Padawer, Feb 16 2023: (Start)

Equals arccot(Pi).

Equals arcsin(1/sqrt(Pi^2 + 1)).

Equals arccos(1/sqrt(1 + 1/Pi^2)). (End)

Example

0.30816907111598493578699960803405309858963702926316931351366234390168...

Mathematica

RealDigits[ArcTan[1/Pi], 10, 90][[1]]

Prog

(PARI) atan(1/Pi) \\ Charles R Greathouse IV, Nov 26 2024

Crossrefs

Cf. A019669, A049541, A232247, A232273.

Sequence in context: A022895 A197416 A197512 * A186744 A200507 A348333

Adjacent sequences: A232269 A232270 A232271 * A232273 A232274 A232275

Keyword

nonn,cons

Author

Bruno Berselli, Nov 22 2013

Status

approved