A242055 Decimal expansion of c, a constant appearing in the asymptotic lower bound of the size of a restricted difference set.

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, 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, 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

Offset: 1

Author

Jean-François Alcover, Aug 13 2014

Keywords

• nonn
• cons

Examples

			1.560277942041879702102077381568463756373995745949542538537...
		

References

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

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants. 2.28 p. 26.

Crossrefs

Cf. A115365.

Programs

Mathematica

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

Formula

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