Primefree sequence

In mathematics, a primefree sequence is a sequence of integers that does not contain any prime numbers. More specifically, it usually means a sequence defined by the same recurrence relation as the Fibonacci numbers, but with different initial conditions causing all members of the sequence to be composite numbers that do not all have a common divisor. To put it algebraically, a sequence of this type is defined by an appropriate choice of two composite numbers a₁ and a₂, such that the greatest common divisor ${\displaystyle \mathrm {gcd} (a_{1},a_{2})}$ is equal to 1, and such that for ${\displaystyle n>2}$ there are no primes in the sequence of numbers calculated from the formula

${\displaystyle a_{n}=a_{n-1}+a_{n-2}}$.

The first primefree sequence of this type was published by Ronald Graham in 1964.