# 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 |
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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 |