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

See also

• Merkle–Hellman knapsack cryptosystem

References

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