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Ulam Numbers

​
u
1
v
2
n
3
1 + 2 = 3
The Ulam numbers (or u-numbers) are the sequence
∞
{
a
n
}
n=0
defined by
a
1
=u
,
a
2
=v
. For
n>2
,
a
n
is the least integer uniquely expressible as the sum of two distinct earlier terms. For example, if
u=1
and
v=2
,
a
3
=3
,
a
4
=4
, and
a
5
=6
;
a
5
≠5
because
5=1+4=2+3
.
This Demonstration shows the Ulam sequence for
u
,
v
, and
n
, highlighting the unique pair of terms that sum to
a
n
.
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