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. ^{[1]}^{[2]}

Formally, written:

## Example Edit

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] sum = 0 test = True for n in sequence: print "Sum: ", sum, "Element: ", n if n <= sum: test = False break sum += n print "Superincreasing sequence? ", test

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

## See also Edit

## References Edit

- ↑ Richard A. Mollin,
*An Introduction to Cryptography (Discrete Mathematical & Applications)*, Chapman & Hall/CRC; 1 edition (August 10, 2000), ISBN 1584881275 - ↑
^{2.0}^{2.1}Bruce Schneier,*Applied Cryptography: Protocols, Algorithms, and Source Code in C*, pages 463-464, Wiley; 2nd edition (October 18, 1996), ISBN 0471117099