OFFSET
0,1
COMMENTS
Let p = sum(sin(k)/k, k>=1) = (Pi-1)/2 (A096444) and q = sum(sin(k/2)/k, k>=1) = (2*Pi-1)/4, then A223709 = (2/3)*p*q.
This is the case h=1 in sum(sin(k/h)/k^3, k>=1) = (h*Pi-1)*(2h*Pi-1)/(12*h^3) = ((h*Pi-1)/(2h))*((2h*Pi-1)/(4h))*(2/(3h)), where (j*Pi-1)/(2j) = sum(sin(k/j)/k, k>=1) and 1/j is real but not an integer multiple of 2Pi.
REFERENCES
Tom M. Apostol, Calculus, Vol. 1, John Wiley & Sons, 1967 (2nd ed.). This constant is the case s=1, t=3 in sum(sin(n*s)/n^t, n>=1), see p. 409.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
Equals sum(sin(k)/k^3, k>=1).
EXAMPLE
0.9428692367841114601900876541594828015029908846963553...
MATHEMATICA
RealDigits[(Pi - 1) (2 Pi - 1)/12, 10, 90][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Bruno Berselli, Mar 26 2013
STATUS
approved