A195793 Decimal expansion of arctan(1000000).

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

Offset

1,2

Comments

pi/2-arctan(1000000)<1/1000000; the first nonzero digits of pi/2-arctan(1000000) are as follows:

999999999999666666666666866666666666. The twelve 6's before 8 correspond to the limit shown at the end of the Mathematica program. What about the next eleven 6's?

Links

Table of n, a(n) for n=1..100.

Example

Let x=pi/2 and y=arc(1000000); then
x=1.57079632679489661923132169163975144209858469968755291048...
y=1.57079532679489661956465502497288477543191817587802910085...
x-y=0.000000099999999999966666666666686666666666652380963492...

Mathematica

N[Pi/2, 100]
N[ArcTan[10^6], 100]
RealDigits[%]  (* A195793 *)
Limit[n^2 - (n^3) (Pi/2 - ArcTan[n]), n -> Infinity]
(* Limit equals 1/3 *)

Crossrefs

Cf. A000796, A195789.

For other approximations to Pi see A216542, A013706, A216543, A216544, A216545, A013705, A216546, A216547, A216548. - N. J. A. Sloane, Sep 08 2012

Sequence in context: A161018 A197254 A013706 * A216545 A216547 A221208

Adjacent sequences: A195790 A195791 A195792 * A195794 A195795 A195796

Keyword

nonn,cons

Author

Clark Kimberling, Sep 24 2011

Status

approved