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.

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

def is_superincreasing_sequence(sequence) -> bool:     """Tests if a sequence is superincreasing."""     total = 0     result = True     for n in sequence:         print("Sum: ", total, "Element: ", n)         if n <= total:             result = False             break         total += n     return result   sequence = [1, 3, 6, 13, 27, 52] result = is_superincreasing_sequence(sequence) print("Is it a superincreasing sequence? ", result) 

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 

• (1, 3, 6, 13, 27, 52) is a superincreasing sequence, but (1, 3, 4, 9, 15, 25) is not.^[2]
• The series a^x for a>=2

• Multiplying a superincreasing sequence by a positive real constant keeps it superincreasing.

• Merkle–Hellman knapsack cryptosystem

This cryptography-related article is a stub. You can help Wikipedia by expanding it.

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