Grossman's Constant

Define the sequence $a_0=1$, $a_1=x$, and

$$a_{n+2}={a_n\over 1+a_{n+1}}$$

for $n\geq 0$. Janssen and Tjaden (1987) showed that this sequence converges for exactly one value of $x$, $x=0.73733830336929\ldots$, confirming Grossman's conjecture.

References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/grssmn/grssmn.html

Janssen, A. J. E. M. and Tjaden, D. L. A. Solution to Problem 86-2. Math. Intel. 9, 40-43, 1987.