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Cullen numbers
A number of the form n⋅2n + 1. more

The Cullen numbers up to 1015 :

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 100000 values, from 1 to 5⋅1030107).

n\r 0  1 
20100000 2 
3333343333433332 3 
409999901 4 
52000020000200002000020000 5 
6033334033334033332 6 
714286142861428614286142841428614286 7 
8099999010000 8 
9111111111211111111111111011110111121111211111 9 
10020000020000020000020000020000 10 
1190929091909090939090909090919091909090919091

A pictorial representation of the table above
motab
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.