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, this condition can be written as
for all n ≥ 1.

Program

The following Python source code tests a sequence of numbers to determine if it is superincreasing:

def is_superincreasing_sequence -> bool:
"""Tests if a sequence is superincreasing."""
total = 0
result = True
for n in sequence:
print
if n <= total:
result = False
break
total += n
return result
sequence =
result = is_superincreasing_sequence
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
Is it a superincreasing sequence? True

Examples

is a superincreasing sequence, but is not.

Properties