Quinn et al. (2007) investigated a class of coupled oscillators whose bifurcation phase offset had a conjectured asymptotic behavior of , with an experimental estimate for the constant as (OEIS A131329). Rather amazingly, Bailey et al. (2007) were able to find a closed form for as the unique root of in the interval , where is a Hurwitz zeta function.
A related constant conjectured by Quinn et al. (2007) to exist was defined in terms of
(1)

and given by
(2)

(OEIS A131330). Even more amazingly, the exact value of this constant was also found by Bailey et al. (2007) without full proof, but with enough to indicate that such a proof could in principle be constructed, to have the exact value
(3)
