<s>
In	O
mathematics	O
,	O
a	O
Somos	B-Algorithm
sequence	I-Algorithm
is	O
a	O
sequence	O
of	O
numbers	O
defined	O
by	O
a	O
certain	O
recurrence	O
relation	O
,	O
described	O
below	O
.	O
</s>
<s>
From	O
the	O
form	O
of	O
their	O
defining	O
recurrence	O
(	O
which	O
involves	O
division	O
)	O
,	O
one	O
would	O
expect	O
the	O
terms	O
of	O
the	O
sequence	O
to	O
be	O
fractions	O
,	O
but	O
nevertheless	O
many	O
Somos	B-Algorithm
sequences	I-Algorithm
have	O
the	O
property	O
that	O
all	O
of	O
their	O
members	O
are	O
integers	O
.	O
</s>
<s>
While	O
in	O
the	O
usual	O
definition	O
of	O
the	O
Somos	B-Algorithm
sequences	I-Algorithm
,	O
the	O
values	O
of	O
ai	O
for	O
ik	O
are	O
all	O
set	O
equal	O
to	O
1	O
,	O
it	O
is	O
also	O
possible	O
to	O
define	O
other	O
sequences	O
by	O
using	O
the	O
same	O
recurrences	O
with	O
different	O
initial	O
values	O
.	O
</s>
<s>
The	O
form	O
of	O
the	O
recurrences	O
describing	O
the	O
Somos	B-Algorithm
sequences	I-Algorithm
involves	O
divisions	O
,	O
making	O
it	O
appear	O
likely	O
that	O
the	O
sequences	O
defined	O
by	O
these	O
recurrence	O
will	O
contain	O
fractional	O
values	O
.	O
</s>
<s>
Nevertheless	O
,	O
for	O
k≤7	O
the	O
Somos	B-Algorithm
sequences	I-Algorithm
contain	O
only	O
integer	O
values	O
.	O
</s>
<s>
Several	O
mathematicians	O
have	O
studied	O
the	O
problem	O
of	O
proving	O
and	O
explaining	O
this	O
integer	O
property	O
of	O
the	O
Somos	B-Algorithm
sequences	I-Algorithm
;	O
it	O
is	O
closely	O
related	O
to	O
the	O
combinatorics	O
of	O
cluster	O
algebras	O
.	O
</s>
