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