Janssen and Tjaden (1987) showed that this sequence converges for exactly one value ,
(OEIS A085835), confirming Grossman's conjecture.
However, no analytic form is known for this constant, either as the root of a function
or as a combination of other constants. The plot above shows the first few iterations
to 30, with odd
shown in red and even shown in blue, for ranging from 0 to 1. As can be seen, the solutions alternate
by parity. For each fixed , the red values go to 0, while the blue values go to
some positive number.
Nyerges (2000) has generalized the recurrence to the functional equation