The double factorials up to 1015 :
1, 2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, 2027025, 10321920, 34459425, 185794560, 654729075, 3715891200, 13749310575, 81749606400, 316234143225, 1961990553600, 7905853580625, 51011754393600, 213458046676875.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 10000 values, from 1 to 5.97⋅1017830).
| n\r | 0 | 1 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 5000 | 5000 | 2 | ||||||||
| 3 | 9997 | 1 | 2 | 3 | |||||||
| 4 | 4999 | 2500 | 1 | 2500 | 4 | ||||||
| 5 | 9994 | 1 | 1 | 3 | 1 | 5 | |||||
| 6 | 4998 | 1 | 2 | 4999 | 0 | 0 | 6 | ||||
| 7 | 9991 | 3 | 1 | 1 | 1 | 0 | 3 | 7 | |||
| 8 | 4999 | 2500 | 1 | 1250 | 0 | 0 | 0 | 1250 | 8 | ||
| 9 | 9991 | 1 | 1 | 2 | 0 | 0 | 4 | 0 | 1 | 9 | |
| 10 | 4996 | 1 | 1 | 1 | 1 | 4998 | 0 | 0 | 2 | 0 | 10 |
| 11 | 9985 | 3 | 1 | 2 | 3 | 0 | 2 | 0 | 1 | 0 | 3 |
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.
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