# 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