cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A195793 Decimal expansion of arctan(1000000).

This page as a plain text file.
%I A195793 #9 Nov 20 2024 23:37:51
%S A195793 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,
%T A195793 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,
%U A195793 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
%N A195793 Decimal expansion of arctan(1000000).
%C A195793 pi/2-arctan(1000000)<1/1000000; the first nonzero digits of pi/2-arctan(1000000) are as follows:
%C A195793 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?
%H A195793 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A195793 Let x=pi/2 and y=arc(1000000); then
%e A195793 x=1.57079632679489661923132169163975144209858469968755291048...
%e A195793 y=1.57079532679489661956465502497288477543191817587802910085...
%e A195793 x-y=0.000000099999999999966666666666686666666666652380963492...
%t A195793 N[Pi/2, 100]
%t A195793 N[ArcTan[10^6], 100]
%t A195793 RealDigits[%]  (* A195793 *)
%t A195793 Limit[n^2 - (n^3) (Pi/2 - ArcTan[n]), n -> Infinity]
%t A195793 (* Limit equals 1/3 *)
%o A195793 (PARI) atan(1e6) \\ _Charles R Greathouse IV_, Nov 20 2024
%Y A195793 Cf. A000796, A195789.
%Y A195793 For other approximations to Pi see A216542, A013706, A216543, A216544, A216545, A013705, A216546, A216547, A216548. - _N. J. A. Sloane_, Sep 08 2012
%K A195793 nonn,cons
%O A195793 1,2
%A A195793 _Clark Kimberling_, Sep 24 2011