Superincreasing sequence


In mathematics, a sequence of positive real numbers is called superincreasing if every element of the sequence is greater than the sum of all previous elements in the sequence.
Formally, written:

Example

For example, is a superincreasing sequence, but is not. The following Python source code tests a sequence of numbers to determine if it is superincreasing:

sequence =
total = 0
test = True
for n in sequence:
print
if n <= total:
test = False
break
total += n
print

This produces the following output:
Sum: 0 Element: 1
Sum: 1 Element: 3
Sum: 4 Element: 6
Sum: 10 Element: 13
Sum: 23 Element: 27
Sum: 50 Element: 52
Superincreasing sequence? True