The n-th hungry number is the smallest k such that the first n decimal digits of π appear in the representation of 2k. more
The hungry numbers up to 10
8 :
5,
17,
74,
144,
2003,
37929,
82810,
161449,
712201,
2401519,
7339199,
33662541.
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 |
A pictorial representation of the table above
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.