A number of the form 4k + 2k+1 - 1. more
The Kynea numbers up to 10
15 :
2,
7,
23,
79,
287,
1087,
4223,
16639,
66047,
263167,
1050623,
4198399,
16785407,
67125247,
268468223,
1073807359,
4295098367,
17180131327,
68720001023,
274878955519,
1099513724927,
4398050705407,
17592194433023,
70368760954879,
281475010265087.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 30000 values, from 2 to 1.567⋅1018061).
n\r | 0 | 1 |
2 | 1 | 29999 | 2 |
3 | 0 | 15000 | 15000 | 3 |
4 | 0 | 0 | 1 | 29999 | 4 |
5 | 0 | 0 | 15000 | 7500 | 7500 | 5 |
6 | 0 | 15000 | 1 | 0 | 0 | 14999 | 6 |
7 | 10000 | 0 | 20000 | 0 | 0 | 0 | 0 | 7 |
8 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 29999 | 8 |
9 | 0 | 0 | 5000 | 0 | 0 | 5000 | 0 | 15000 | 5000 | 9 |
10 | 0 | 0 | 1 | 7500 | 0 | 0 | 0 | 14999 | 0 | 7500 | 10 |
11 | 0 | 6000 | 6000 | 6000 | 0 | 0 | 0 | 6000 | 0 | 3000 | 3000 |
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.