<s>
In	O
mathematics	O
,	O
the	O
Wythoff	B-Algorithm
array	I-Algorithm
is	O
an	O
infinite	O
matrix	B-Architecture
of	O
integers	O
derived	O
from	O
the	O
Fibonacci	B-Algorithm
sequence	I-Algorithm
and	O
named	O
after	O
Dutch	O
mathematician	O
Willem	O
Abraham	O
Wythoff	O
.	O
</s>
<s>
The	O
Wythoff	B-Algorithm
array	I-Algorithm
was	O
first	O
defined	O
by	O
using	O
Wythoff	O
pairs	O
,	O
the	O
coordinates	O
of	O
winning	O
positions	O
in	O
Wythoff	O
's	O
game	O
.	O
</s>
<s>
It	O
can	O
also	O
be	O
defined	O
using	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
and	O
Zeckendorf	B-Algorithm
's	I-Algorithm
theorem	I-Algorithm
,	O
or	O
directly	O
from	O
the	O
golden	O
ratio	O
and	O
the	O
recurrence	O
relation	O
defining	O
the	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
.	O
</s>
<s>
Inspired	O
by	O
a	O
similar	O
Stolarsky	O
array	O
previously	O
defined	O
by	O
,	O
defined	O
the	O
Wythoff	B-Algorithm
array	I-Algorithm
as	O
follows	O
.	O
</s>
<s>
The	O
Zeckendorf	B-Algorithm
representation	I-Algorithm
of	O
any	O
positive	O
integer	O
is	O
a	O
representation	O
as	O
a	O
sum	O
of	O
distinct	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
,	O
no	O
two	O
of	O
which	O
are	O
consecutive	O
in	O
the	O
Fibonacci	B-Algorithm
sequence	I-Algorithm
.	O
</s>
<s>
As	O
describes	O
,	O
the	O
numbers	O
within	O
each	O
row	O
of	O
the	O
array	O
have	O
Zeckendorf	B-Algorithm
representation	I-Algorithm
that	O
differ	O
by	O
a	O
shift	O
operation	O
from	O
each	O
other	O
,	O
and	O
the	O
numbers	O
within	O
each	O
column	O
have	O
Zeckendorf	B-Algorithm
representations	I-Algorithm
that	O
all	O
use	O
the	O
same	O
smallest	O
Fibonacci	B-Algorithm
number	I-Algorithm
.	O
</s>
<s>
In	O
particular	O
the	O
entry	O
of	O
the	O
array	O
is	O
the	O
th	O
smallest	O
number	O
whose	O
Zeckendorf	B-Algorithm
representation	I-Algorithm
begins	O
with	O
the	O
th	O
Fibonacci	B-Algorithm
number	I-Algorithm
.	O
</s>
<s>
Each	O
Wythoff	O
pair	O
occurs	O
exactly	O
once	O
in	O
the	O
Wythoff	B-Algorithm
array	I-Algorithm
,	O
as	O
a	O
consecutive	O
pair	O
of	O
numbers	O
in	O
the	O
same	O
row	O
,	O
with	O
an	O
odd	O
index	O
for	O
the	O
first	O
number	O
and	O
an	O
even	O
index	O
for	O
the	O
second	O
.	O
</s>
<s>
Every	O
sequence	O
of	O
positive	O
integers	O
satisfying	O
the	O
Fibonacci	O
recurrence	O
occurs	O
,	O
shifted	O
by	O
at	O
most	O
finitely	O
many	O
positions	O
,	O
in	O
the	O
Wythoff	B-Algorithm
array	I-Algorithm
.	O
</s>
<s>
In	O
particular	O
,	O
the	O
Fibonacci	B-Algorithm
sequence	I-Algorithm
itself	O
is	O
the	O
first	O
row	O
,	O
and	O
the	O
sequence	O
of	O
Lucas	B-Algorithm
numbers	I-Algorithm
appears	O
in	O
shifted	O
form	O
in	O
the	O
second	O
row	O
.	O
</s>
