login
A242055
Decimal expansion of c, a constant appearing in the asymptotic lower bound of the size of a restricted difference set.
0
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
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.28 p. 188.
FORMULA
c = sqrt(2*(1 - sin(theta)/theta)), where theta is the smallest positive zero of tan(t)-t (theta = A115365).
EXAMPLE
1.560277942041879702102077381568463756373995745949542538537...
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
CROSSREFS
Cf. A115365.
Sequence in context: A100220 A011440 A375957 * A178591 A179588 A092161
KEYWORD
nonn,cons
AUTHOR
STATUS
approved