Upon reading the question, power of primes immediately come to mind,
2, 4, 8, 16, ... works, but we hit the 1e18 constraint pretty quickly, need to include powers of more primes,
One way is to start from cube of a prime, them when this primes constraint hits, we add a link element between the powers of this prime and the next prime, Link element = p*p*q, p is the prime whose constraint we just hit and q is the next prime.
So link between 2's power's and 3's power's would be 12.
Solution: https://mirror.codeforces.com/contest/2218/submission/370051646
How about we do 2 4 8 16 then as we hit 1e18 constraint we do 3 6 12 .... then 5 10 20 ...?
gcd (last element of 2,4,8,16.... series,3) == 1
You can multiply last element the series 2, 4, 8, 16 ... by 3 and continue the series with 3^2, 3^3, 3^4...