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

Author

Clark Kimberling, Sep 24 2011

Keywords

• nonn
• cons

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?

Examples

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

Links

• Index entries for transcendental numbers

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

Programs

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 *)

PARI

atan(1e6) \\ Charles R Greathouse IV, Nov 20 2024