# Superincreasing sequence

In mathematics, a sequence of positive real numbers ${\displaystyle (s_{1},s_{2},...)}$ is called superincreasing if every element of the sequence is greater than the sum of all previous elements in the sequence.[1][2]

Formally, this condition can be written as

${\displaystyle s_{n+1}>\sum _{j=1}^{n}s_{j}}$

for all n ≥ 1.

## Example

For example, (1, 3, 6, 13, 27, 52) is a superincreasing sequence, but (1, 3, 4, 9, 15, 25) is not.[2] The following Python source code tests a sequence of numbers to determine if it is superincreasing:

sequence = [1, 3, 6, 13, 27, 52]
total = 0
test = True
for n in sequence:
print("Sum: ", total, "Element: ", n)
if n <= total:
test = False
break
total += n

print("Superincreasing sequence? ", test)


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


## References

1. ^ Richard A. Mollin, An Introduction to Cryptography (Discrete Mathematical & Applications), Chapman & Hall/CRC; 1 edition (August 10, 2000), ISBN 1-58488-127-5
2. ^ a b Bruce Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C, pages 463-464, Wiley; 2nd edition (October 18, 1996), ISBN 0-471-11709-9