<s>
In	O
mathematics	O
,	O
the	O
Jacobsthal	B-Algorithm
numbers	I-Algorithm
are	O
an	O
integer	O
sequence	O
named	O
after	O
the	O
German	O
mathematician	O
Ernst	O
Jacobsthal	O
.	O
</s>
<s>
Like	O
the	O
related	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
,	O
they	O
are	O
a	O
specific	O
type	O
of	O
Lucas	B-Algorithm
sequence	I-Algorithm
for	O
which	O
P	O
=	O
1	O
,	O
and	O
Q	O
=	O
2	O
—	O
and	O
are	O
defined	O
by	O
a	O
similar	O
recurrence	O
relation	O
:	O
in	O
simple	O
terms	O
,	O
the	O
sequence	O
starts	O
with	O
0	O
and	O
1	O
,	O
then	O
each	O
following	O
number	O
is	O
found	O
by	O
adding	O
the	O
number	O
before	O
it	O
to	O
twice	O
the	O
number	O
before	O
that	O
.	O
</s>
<s>
The	O
first	O
Jacobsthal	B-Algorithm
numbers	I-Algorithm
are	O
:	O
</s>
<s>
A	O
Jacobsthal	B-Algorithm
prime	I-Algorithm
is	O
a	O
Jacobsthal	B-Algorithm
number	I-Algorithm
that	O
is	O
also	O
prime	O
.	O
</s>
<s>
The	O
first	O
Jacobsthal	B-Algorithm
primes	I-Algorithm
are	O
:	O
</s>
<s>
Jacobsthal	B-Algorithm
numbers	I-Algorithm
are	O
defined	O
by	O
the	O
recurrence	O
relation	O
:	O
</s>
<s>
The	O
Jacobsthal	B-Algorithm
number	I-Algorithm
at	O
a	O
specific	O
point	O
in	O
the	O
sequence	O
may	O
be	O
calculated	O
directly	O
using	O
the	O
closed-form	O
equation	O
:	O
</s>
<s>
The	O
sum	O
of	O
the	O
reciprocals	O
of	O
the	O
Jacobsthal	B-Algorithm
numbers	I-Algorithm
is	O
approximately	O
2.7186	O
,	O
slightly	O
larger	O
than	O
e	O
.	O
</s>
<s>
Jacobsthal	B-Algorithm
–	I-Algorithm
Lucas	I-Algorithm
numbers	I-Algorithm
represent	O
the	O
complementary	O
Lucas	B-Algorithm
sequence	I-Algorithm
.	O
</s>
<s>
They	O
satisfy	O
the	O
same	O
recurrence	O
relation	O
as	O
Jacobsthal	B-Algorithm
numbers	I-Algorithm
but	O
have	O
different	O
initial	O
values	O
:	O
</s>
<s>
The	O
following	O
Jacobsthal	B-Algorithm
–	I-Algorithm
Lucas	I-Algorithm
number	I-Algorithm
also	O
satisfies	O
:	O
</s>
<s>
The	O
Jacobsthal	B-Algorithm
–	I-Algorithm
Lucas	I-Algorithm
number	I-Algorithm
at	O
a	O
specific	O
point	O
in	O
the	O
sequence	O
may	O
be	O
calculated	O
directly	O
using	O
the	O
closed-form	O
equation	O
:	O
</s>
<s>
The	O
first	O
Jacobsthal	B-Algorithm
–	I-Algorithm
Lucas	I-Algorithm
numbers	I-Algorithm
are	O
:	O
</s>
