Last updated Evolution of the sequence for several values of , around the Foias constant . Evolution for is in green. Other initial values lead to two accumulation points, 1 and . A logarithmic scale is used.
for n = 1, 2, 3, .... The Foias constant is the unique choice α such that if x1=α then the sequence diverges to infinity. For all other values of x1, the sequence is divergent as well, but it has two accumulation points: 1 and infinity.[1] Numerically, it is
1 2 Ewing, J. and Foias, C. "An Interesting Serendipitous Real Number." In Finite versus Infinite: Contributions to an Eternal Dilemma (Ed. C. Caluse and G. Păun). London: Springer-Verlag, pp. 119–126, 2000.
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![Evolution of the sequence
x
n
+
1
=
(
1
+
1
/
x
n
)
n
{\displaystyle x_{n+1}=(1+1/x_{n})^{n}}
for several values of
x
1
{\displaystyle x_{1}}
, around the Foias constant
a
{\displaystyle \alpha }
. Evolution for
x
1
=
a
{\displaystyle x_{1}=\alpha }
is in green. Other initial values lead to two accumulation points, 1 and
[?]
{\displaystyle \infty }
. A logarithmic scale is used. Foias constant sequence.png](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Foias_constant_sequence.png/400px-Foias_constant_sequence.png)
