Numbers that add to generate any other number Here I would like to state about the numbers $3$ and $5$,which by the help of addition(any number of times) can generate any number from $8(=5+3)$ on-wards.
For example:
$9 = 3 + 3 +3$
$10 = 5+5$
$11=5+3+3$
and so on.Further we know that if we can generate any nine consecutive numbers then we can generate further numbers from the ninth number onward by addition.Hence this pair (3,5) has this ability.
My Question :
Is there any name for these kind of pairs?Further is there any method to find such pairs?

Such pair is called co-prime and a special case of an additive base $\mathcal{B}$ of the natural numbers. Every subset of the natural numbers is called an additive base $\mathcal{B}$ if there is a natural number $h$ such that every sufficiently large natural number $n$ can be constructed as sum of at most $h$ numbers from $\mathcal{B}$.
The largest number that cannot be constructed using this set given $h$ is called Frobenius number.
Answering your question, any pair of co-prime numbers will possess this property. Let $a, b$ be co-prime, then given their Frobenius number $ab -a - b$ all subsequent integers $n > ab -a - b$ can be represented as linear combination $n = ax + by$ of $a$ and $b$ with non-negative integer coefficients $x$ and $y$.
