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Superincreasing sequence

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.

Formally, this condition can be written as

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

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

Properties

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

See also

References