A289505 Decimal expansion of arcsec(3)/(2*Pi).

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

Offset: 0

Author

R. J. Mathar, Jul 07 2017

Keywords

• nonn
• cons
• easy

Examples

			0.195913276015303635085427779611215...
		

Links

• Steven R. Finch, Mean width of a regular simplex, arxiv:1111.4976 [math.MG], 2011-2016, S_2.
• W. V. Gehrlein, Condorcet's paradox and the Condorcet efficiency of voting rules, Mathematica Japonica 45, 173-199, 1997.

Crossrefs

Cf. A086201, A137914.

Programs

Maple

arcsec(3)/2/Pi ; evalf(%) ;

Mathematica

RealDigits[ArcSec[3]/(2 Pi),10,120][[1]] (* Harvey P. Dale, Jul 21 2021 *)

PARI

acos(1/3)/(2*Pi) \\ Michel Marcus, Jul 07 2017

Python

from mpmath import mp, asec, pi
mp.dps=89
print([int(z) for z in list(str(asec(3)/(2*pi))[2:-1])]) # Indranil Ghosh, Jul 07 2017

Formula

Equals A137914*A086201.

From Robert FERREOL, Mar 21 2018: (Start)

Equals arctan(2*sqrt(2))/(2*Pi).

Equals (1/(2*Pi))*Integral_{t>=sqrt(2)/4} 1/(1+t^2).

Equals Probability(X>sqrt(2)/4)/2, if X is a Cauchy distributed random variable of location parameter 0 and scale parameter 1.

Equals the asymptotic probability p that A is predominantly preferred to B and B predominantly preferred to C when n persons provide a preference list of three candidates A, B, C (with a uniform distribution on voter preferences); the asymptotic probability that A > B > C > A or A > C > B > A (where ">" means "predominantly preferred to") is 3p-1/2 = 8.77...% (Condorcet paradox); the contrary probability (existence of a Condorcet winner) is 3/2-3p = 91.226...%.

See Gehrlein link. (End)