# A brief int counter

The following infinite sequence is used by those taking first steps in maths.

3, 3, 4, 4, 4, 3, 4, 5, 3, 3, 4, 5, 6, 7, ?

Find the next number.

• +1 just for the title! – Arth May 23 '18 at 8:22

$5$
The number of unique letters in the English spelling of each of the cardinal numbers, e.g, $3 \rightarrow$ THREE which has $4$ unique letters: 'T','H','R' and 'E'.
The next number, $15$, has $5$ unique letters in its spelling: 'F', 'I', 'T', 'E' and 'N', hence the answer is $5$.