I`m not sure, if this is the right category, but...
For every positive integer i, ai is the greatest divisor of i which is not
is divisible by 3. The sequence (sm) is defined by sm := a1 +a2 + . . . + am.
Proofs: The number sm is divisible by 3 precisely if the number of ones in the representation of m in the ternary system is divisible by 3.
(For example s5 = 1 + 2 + 1 + 4 + 5)
My approaches are:
1. A number is divisible by three if it is its cross sum.
2. A number in the ternary system looks like this: a30 b31 c32 ..., so if the ones in the representation are divisible by three, there are either no ones or 3x ones.
I would be very grateful for ideas or suggestions for solutions.
For every positive integer i, ai is the greatest divisor of i which is not
is divisible by 3. The sequence (sm) is defined by sm := a1 +a2 + . . . + am.
Proofs: The number sm is divisible by 3 precisely if the number of ones in the representation of m in the ternary system is divisible by 3.
(For example s5 = 1 + 2 + 1 + 4 + 5)
My approaches are:
1. A number is divisible by three if it is its cross sum.
2. A number in the ternary system looks like this: a30 b31 c32 ..., so if the ones in the representation are divisible by three, there are either no ones or 3x ones.
I would be very grateful for ideas or suggestions for solutions.