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Homesuperincreasing sequence

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# superincreasing sequence

A sequence $\{s_{j}\}$ of real numbers is *superincreasing* if $\displaystyle s_{{n+1}}>\sum_{{j=1}}^{n}s_{j}$ 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 $\displaystyle x=\sum_{{j=1}}^{n}a_{j}s_{j}$. 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.

Related:

Superconvergence

Synonym:

superincreasing

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11B83*no label found*

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