That could be because they are actually powers of 11...

11

^{0}= 1

11

^{1}= 11

11

^{2}= 121

11

^{3}= 1331

11

^{4}= 14641

But what is 11

^{5}? Whoa - hold up. Let's recap just a little...

Let's re-examine 11

^{2}....

What we are really seeing is:

10^{2} | 10^{1} | 10^{0} |
---|---|---|

1 | 2 | 1 |

Which is really... | ||

1 * 10^{2} | 2 * 10^{1} | 1 * 10^{0} |

100 | 20 | 1 |

or... 100+20+1 = 121 = 11^{2} |

The same is true for 11

^{3}...

10^{3} | 10^{2} | 10^{1} | 10^{0} |
---|---|---|---|

1 | 3 | 3 | 1 |

Which is really... | |||

1 * 10^{3} | 3 * 10^{2} | 3 * 10^{1} | 1 * 10^{0} |

1000 | 300 | 30 | 1 |

or... 1000+300+30+1 = 1331 = 11^{3} |

Now, 11

^{5}is a bit more tricky... The math is the exact same, but it is not as visually obvious...

10^{5} | 10^{4} | 10^{3} | 10^{2} | 10^{1} | 10^{0} |
---|---|---|---|---|---|

1 | 5 | 10 | 10 | 5 | 1 |

Which is really... | |||||

1 * 10^{5} | 5 * 10^{4} | 10 * 10^{3} | 10 * 10^{2} | 5 * 10^{1} | 1 * 10^{0} |

100000 | 50000 | 10000 | 1000 | 50 | 1 |

or... 100000+50000+10000+1000+50+1 = 161051 = 11^{5} |