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The hungry numbers up to 10

__Distribution of the remainders__ when the numbers in this family are divided by *n*=2, 3,..., 11. (I took into account 12 values, from 5 to 33662541).

n\r | 0 | 1 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

2 | 3 | 9 | 2 | ||||||||

3 | 3 | 4 | 5 | 3 | |||||||

4 | 1 | 6 | 2 | 3 | 4 | ||||||

5 | 2 | 2 | 1 | 1 | 6 | 5 | |||||

6 | 1 | 3 | 1 | 2 | 1 | 4 | 6 | ||||

7 | 3 | 3 | 0 | 3 | 2 | 1 | 0 | 7 | |||

8 | 1 | 4 | 2 | 1 | 0 | 2 | 0 | 2 | 8 | ||

9 | 1 | 1 | 1 | 2 | 2 | 3 | 0 | 1 | 1 | 9 | |

10 | 1 | 2 | 0 | 1 | 2 | 1 | 0 | 1 | 0 | 4 | 10 |

11 | 1 | 3 | 2 | 0 | 0 | 1 | 2 | 0 | 1 | 0 | 2 |

Imagine to divide the members of this family by a number *n* and compute the remainders. Should they be uniformly distributed, each remainder from 0 to *n*-1 would be obtained in about (1/*n*)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/*n*.

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