In mathematics, a sequence of positive real numbers ( s 1 , s 2 , . . . ) {\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. Formally, this condition can be written as
s n + 1 > ∑ j = 1 n s j {\displaystyle s_{n+1}>\sum _{j=1}^{n}s_{j}}
for all n ≥ 1.
Program The following Python source code tests a sequence of numbers to determine if it is superincreasing:
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 (1, 3, 6, 13, 27, 52) is a superincreasing sequence, but (1, 3, 4, 9, 15, 25) is not. The series a^x for a>=2
Properties Multiplying a superincreasing sequence by a positive real constant keeps it superincreasing.
See also Merkle–Hellman knapsack cryptosystem
References