A242055 - OEIS

%I #13 Jan 17 2020 05:42:16

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

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

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

%N Decimal expansion of c, a constant appearing in the asymptotic lower bound of the size of a restricted difference set.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.28 p. 188.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> 2.28 p. 26.

%F c = sqrt(2*(1 - sin(theta)/theta)), where theta is the smallest positive zero of tan(t)-t (theta = A115365).

%e 1.560277942041879702102077381568463756373995745949542538537...

%t digits = 103; theta = t /. FindRoot[Tan[t] == t, {t, 4}, WorkingPrecision -> digits+5]; c = Sqrt[2*(1 - Sin[theta]/theta)]; RealDigits[c, 10, digits] // First

%Y Cf. A115365.

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, Aug 13 2014