Question 60
Consider increasing integer sequences with elements from $1, \dots, 10^9$. Such a sequence is Adriatic if its first element equals $1$ and if every element is at least twice the preceding element. A sequence is Tyrrhenian if its final element equals $10^6$ and if every element is strictly greater than the sum of all preceding elements. Decide whether the number of elements of Adriatic sequences is (i) smaller than or (ii) equal to or (iii) greater than the number of Tyrrhenian sequences.