And, because of this, the very first symbols used must be concepts that need no definition. They must be universal in the true sense of the word. Civilisations throughout history all learnt to count before they invented written language. The Incas, for example, never set stylus to clay or pen to papyrus, but used a system of knots in strings. Civilisation after civilisation discovered the same numerical properties, derived the same theorems and used the same mathematical tools.
Numbers are the closest thing humans have to a cultural universal.
So, in his message, which is based on Lincos, Dutil starts by showing the aliens that he can count. If the aliens have even a primitive mathematical system, they should know this sequence. Better yet, the sequence of numbers is irregular, not the sort of thing that would come from a natural source such as a pulsar. From the first page, the aliens should understand how we represent numbers. This gives them an idea of the notation we use.