(In reply to

computer solution by Charlie)

a. Your count of possible solutions to a*b solutions is correct, **mine** and Jer's are **not **, counting twice the part with negative numbers.

b. However since "**arithmetic progression** is a sequence of numbers such that the difference of any two successive members of the sequence is a constant" the first two entries hardly qualify:

2016 - there are no successive members,

1007,1009 - no **constant **difference.

So the total number of arithmetic sequences is **34**.