superincreasing sequence

A sequenceMathworldPlanetmath {sj} of real numbers is superincreasing if sn+1>j=1nsj for every positive integer n. That is, any element of the sequence is greater than all of the previous elements added together.

A commonly used superincreasing sequence is that of powers of two (sn=2n.)

Suppose that x=j=1najsj. If {sj} is a superincreasing sequence and every aj{0,1}, then we can always determine the aj’s simply by knowing x. This is analogous to the fact that, for any natural numberMathworldPlanetmath, we can always determine which bits are on and off in the binary bitstring representing the number.

Title superincreasing sequence
Canonical name SuperincreasingSequence
Date of creation 2013-03-22 11:55:22
Last modified on 2013-03-22 11:55:22
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 10
Author Wkbj79 (1863)
Entry type Definition
Classification msc 11B83
Synonym superincreasing
Related topic Superconvergence