Q: n is a none-negative numbers, in order to let divides perfectly 7, characterise n.
A: in binary representation is n ones. And 7 in binary is 111. The n has to be multiples of 3 in order for to be zero.
The following python script proves this by output the first then n (excluding zero because it is so obvious)
#!/usr/bin/python cnt = 0 n = 1 while 1: if (2**n - 1) % 7 == 0: cnt += 1 print n if cnt > 10: break n += 1
It will output 3, 6, 9, 12 … 33. can be replaced by bit logics operation , which is a lot faster.
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