superincreasing sequence

A sequence $\{s_j\}$ of real numbers is superincreasing if $s_{n+1}>{\displaystyle \sum _{j=1}^n}{s}_j$ 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 ($s_n=2^n$.)

Suppose that $x={\displaystyle \sum _{j=1}^n}{a}_j{s}_j$. If $\{s_j\}$ is a superincreasing sequence and every $a_j\in \{0,1\}$, then we can always determine the $a_j$’s simply by knowing $x$. This is analogous to the fact that, for any natural number, 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